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“Practice makes perfect,” prepare a stronger base for algebra with this assemblage of pre-algebra worksheets; featuring exercises on topics like fractions, decimals, integers, measurement, squaring numbers, order of operations, estimation, factors, GCF, LCM, ratio, percent, exponents, radicals, scientific notations, logarithms, absolute value, graph and more.
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- Greatest common Factors (GCF)
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Factoring Worksheets
Gain immense practice with this batch of factoring worksheets. Learn to list out factors, find the prime factors, the Greatest Common Factor (GCF), the Least Common Multiple (LCM), draw the factor tree and much more.
Greatest common Factor (GCF) Worksheets
A collection of tailor-made GCF worksheets aimed at providing an in-depth knowledge of finding the GCF of two and three numbers, the GCF of monomials and GCF of polynomials. Venn-diagrams and factor trees can be used for a better understanding of the concept.
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Converting between Fractions and Decimals Worksheets
Flex your learning parameters with this exhaustive collection of practice worksheets and solidify skills in converting between fractions and decimals with clarity and accuracy.
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Percent Worksheets
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Convert between Fractions, Decimals, and Percents Worksheets
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This vast collection of printable proportion worksheets gives a clear understanding of the concept of proportion with exercises to identify and form a proportion, plot the graph, find the constant of proportionality, and word problems pertaining to proportion.
Direct and Inverse Variation Worksheets
This assemblage of direct and inverse variation worksheets features direct, inverse, combined and joint variations. Ample exercises to identify the type of variation, finding the constant; translating equations and real-life word problems are included as well.
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Perform a combination of arithmetic operations on 3 numbers with 2 operators, 4 numbers with 3 operators, with parentheses and nested parentheses; simplify decimals and fractions using PEMDAS, BODMAS or DMAS.
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Scientific Notation Worksheets
Equip yourself in writing scientific notations with this unit of pre-algebra worksheets, featuring tasks to rewrite scientific notations as standard form and vice-versa with positive, negative and mixed exponents. Simplify scientific notations as well.
Conversion of Units of Speed Worksheets
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2.3e: Exercises - Transformations
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A: Concepts
Exercise \(\PageIndex{A}\)
1) When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift? 2) When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch? 3) When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression? 4) When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the \(x\)-axis from a reflection with respect to the \(y\)-axis? 5) How can you determine whether a function is odd or even from the formula of the function?
1. A horizontal shift results when a constant is added to or subtracted from the input. A vertical shifts results when a constant is added to or subtracted from the output.
3. A horizontal compression results when a constant greater than \(1\) is multiplied by the input. A vertical compression results when a constant between \(0\) and \(1\) is multiplied by the output.
5. For a function \(f\), substitute (−x) for (x) in \(f(x)\). Simplify. If the resulting function is the same as the original function, \(f(−x)=f(x)\), then the function is even. If the resulting function is the opposite of the original function, \(f(−x)=−f(x)\), then the original function is odd. If the function is not the same or the opposite, then the function is neither odd nor even.
B: Describe transformations of a function written in function notation
Exercise \(\PageIndex{B}\)
\( \bigstar\) Describe how the graph of the function is a transformation of the graph of the original function \(f\).
7. The graph of \(f(x+43)\) is a horizontal shift to the left \(43\) units of the graph of \(f\).
9. The graph of \(f(x-4)\) is a horizontal shift to the right \(4\) units of the graph of \(f\).
11. The graph of \(f(x)+8\) is a vertical shift up \(8\) units of the graph of \(f\).
13. The graph of \(f(x)−7\) is a vertical shift down \(7\) units of the graph of \(f\).
15. The graph of \(f(x+4)−1\) is a horizontal shift left \(4\) units and vertical shift down \(1\) unit of the graph of \(f\).
17. The graph of \(g\) is a vertical reflection (across the x-axis) of the graph of \(f\).
19. The graph of \(g\) is a vertical stretch by a factor of 4 of the graph of \(f\).
21. The graph of \(g\) is a horizontal compression by a factor of \(\frac{1}{5}\) of the graph of \(f\).
23. The graph of \(g\) is a horizontal stretch by a factor of 3 of the graph of \(f\).
25. The graph of \(g\) is a horizontal reflection across the y-axis and a vertical stretch by a factor of 3 of the graph of \(f\).
C: Graph transformations of a basic function
Exercise \(\PageIndex{C}\)
\( \bigstar\) Begin by graphing the basic quadratic function \(f(x)=x^2\). State the transformations needed to apply to \(f\) to graph the function below. Then use transformations to graph the function.
\( \bigstar\) Begin by graphing the square root function \(f(x)=\sqrt{x}\). State the transformations needed to apply to \(f\) to graph the function below. Then use transformations to graph the function.
\( \bigstar\) Begin by graphing the absolute value function \(f(x)=| x |\). State the transformations needed to apply to \(f\) to graph the function below. Then use transformations to graph the function.
\( \bigstar\) Begin by graphing the standard cubic function \(f(x) = x^3 \). State the transformations needed to apply to \(f\) to graph the function below. Then use transformations to graph the function.
\( \bigstar\) Begin by graphing the appropriate parent function : the basic cube root function \(f(x)=\sqrt[3]{x}\), constant function \(f(x)=0\), or linear function \(f(x)=x\). Then use transformations of this graph to graph the given function.
\( \bigstar\) Begin by graphing the basic reciprocal function \(f(x)=\frac{1}{x}\). State the transformations needed to apply to \(f\) to graph the function below. Then use transformations to graph the function.
Square Root Function
Absolute Value Function
Cubing Function
Cube Root, Linear, Constant Functions
Reciprocal Function
D: Graph Transformations of a Graph
Exercise \(\PageIndex{D}\)
\( \bigstar\) Use the graph of \(f(x)\) shown in the Figure below to sketch a graph of each transformation of \(f(x)\).
106. Given the graph of \(f(x)\) below, sketch the graph for the following transformations of \(f\)
E: Match transformations of functions with graphs
Exercise \(\PageIndex{E}\)
\( \bigstar\) Match the graph to the function definition.
Match the graph to the given function definition.
part 1 answers 107e, 109d, 111f, part 2 Answers: 113.b, 115.d, 117.f
F: Construct equations from graphs of transformed basic functions
Exercise \(\PageIndex{F}\)
\( \bigstar\) Write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions.
\( \bigstar\) Write an equation that represents the function whose graph is given.
G: Construct a formula from a description
Exercise \(\PageIndex{G}\)
\( \bigstar\) Write a formula for the function with the following transformations
141. Write a formula for the function obtained when the graph of \(f(x)=|x|\) is shifted down \(3\) units and right \(1\) unit.
142. Write a formula for the function obtained when the graph of \(f(x)=\dfrac{1}{x}\) is shifted down \(4\) units and right \(3\) units.
143. Write a formula for the function obtained when the graph of \(f(x)=\dfrac{1}{x^2}\) is shifted up \(2\) units and left \(4\) units.
144. Write a formula for the function obtained when the graph of \(f(x)=\sqrt{x}\) is shifted up \(1\) unit and left \(2\) units.
145. The graph of \(f(x)=|x|\) is reflected over the \(y\)-axis and horizontally compressed by a factor of \(\dfrac{1}{4}\).
146. The graph of \(f(x)=\sqrt{x}\) is reflected over the \(x\)-axis and horizontally stretched by a factor of \(2\).
147. The graph of \(f(x)=\dfrac{1}{x^2}\) is vertically compressed by a factor of \(\dfrac{1}{3}\), then shifted left \(2\) units and down \(3\) units.
148. The graph of \(f(x)=\dfrac{1}{x}\) is vertically stretched by a factor of \(8\), then shifted to the right \(4\) units and up \(2\) units.
149. The graph of \(f(x)=x^2\) is vertically compressed by a factor of \(\dfrac{1}{2}\), then shifted to the right \(5\) units and up \(1\) unit.
150. The graph of \(f(x)=x^2\) is horizontally stretched by a factor of \(3\), then shifted left \(4\) units and down \(3\) units.
H: Construct equations from transformations of tabular values
Exercise \(\PageIndex{H}\)
\( \bigstar\) Given tabular representations for the functions \(f\), \(g\), and \(h\), write \(g(x)\) and \(h(x)\) as transformations of \(f(x)\).
155. Tabular representations for the functions \(f\), \(g\), and \(h\) are given below. Write \(g(x)\) and \(h(x)\) as transformations of \(f(x)\).
156. Tabular representations for the functions \(f\), \(g\), and \(h\) are given below. Write \(g(x)\) and \(h(x)\) as transformations of \(f(x)\).
155. \(g(x)=f(x-1)\), \(h(x)=f(x)+1\).
I: Identify Increasing/decreasing Intervals
Exercise \(\PageIndex{I}\)
\( \bigstar\) Use transformations to determine the interval(s) on which the function is increasing and decreasing.
\( \star \)
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Free Printable Math Worksheets for Pre-Algebra Created with Infinite Pre-Algebra Stop searching. Create the worksheets you need with Infinite Pre-Algebra. Fast and easy to use Multiple-choice & free-response Never runs out of questions Multiple-version printing Free 14-Day Trial Windows macOS Basics Naming decimal places
14) reflection across the x-axis. origin. Pre-Algebra. TRANSFORMATIONS. ©Z A2a0e1v53 bKmuftnaM MSuoBfEtVweaPrNe3 iLfLkCe.D j AA0lxll Kr9iWgIhwtJsT PrCegske9rVvzeVdO.T. Write a rule to describe each transformation. 1) y. B'. A' N'.
Z'(−1, 1), I'(1, 2), V'(1, 0) translation: 4 units up translation: 3 units right and 3 units down translation: 4 units left and 2 units up translation: 6 units right Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC-2-Scale factor is 2.5. Is the figure being reduced or enlarged? What would be the new base measurement? 6) 3 cm 3 cm Graph the image of the figure using the transformation given. 7) translation: 5 units left and 3 units down x y Y F N 8) translation: (x, y) ® (x + 5, y + 3) x y Q E M 9) reflection across the y ...
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These assessments were designed for a middle school pre-algebra unit on transformations and similar figures. Included is a practice test for review, 2 versions of a unit assessment and an answer key for each document. ... Hello Math Teachers! This worksheet is on making two consecutive transformations of points, lines segments, and polygons by ...
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"Practice makes perfect," prepare a stronger base for algebra with this assemblage of pre-algebra worksheets; featuring exercises on topics like fractions, decimals, integers, measurement, squaring numbers, order of operations, estimation, factors, GCF, LCM, ratio, percent, exponents, radicals, scientific notations, logarithms, absolute value, g...
W'(4, 5), K'(3, 2), F'(4, 2) Z'(1, 2), G'(−1, 3), M'(−3, 1), V'(1, −1) reflection across x = −2 reflection across the y-axis reflection across x = −2 reflection across x = 2 Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
MTH 165 College Algebra, MTH 175 Precalculus 2: Functions and Their Graphs 2.3: Transformations of Functions ... Write a formula for the function with the following transformations. 141. Write a formula for the function obtained when the graph of \(f(x)=|x|\) is shifted down \(3\) units and right \(1\) unit.
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reflection across the x-axis reflection across y = − x. reflection across x = −3. reflection across the y-axis reflection across y = x. Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com.
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