Given the parent function f(x) and descriptions of the transformations, write the equation of the transformed function, g(x). (Transformation should go in the described order.) f(x)=x3; vertical streetch by a factor 2.5, reflection over y-axis, horizontal translation left1.

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Given the parent function f(x) and descriptions of the transformations, write the equation of the transformed function, g(x). (Transformation should go in the described order.)  f(x)=x3; vertical streetch by a factor 2.5, reflection over y-axis, horizontal translation left1.

Nicole Conner · Accepted Answer

Step 1  Given function is f(x)=x3  To write the equation of transformed function.  Solution:  Given function is f(x)=x3.  We know that when y=f(x) is stretched vertically by c units then function becomes y=cf(x).  So, when function f(x)=x3 is strectched vertically by 2.5 then function will becomes y=(2.5)x3  Step 1  Given function is f(x)=x3  To write the equation of transformed function.  Solution:  Given function is f(x)=x3.  We know that when y=f(x) is stretched vertically by c units then function becomes y=cf(x).  So, when function f(x)=x3 is strectched vertically by 2.5 then function will becomes y=(2.5)  Now, the graph of the function y=f(−x) is the graph of y=f(x) reflected in the y-axis.  So, when y=(2.5)x3 isreflected in the y−axis then function will become y=(2.5)(−x)3 And if c is positive real number then graph of f(x−c) is the graph of y=f(x) shifted horizontally by c units.  So, when y=(2.5)(−x)3 is shifted left by 1 unit then function will be g(x)=(2.5)(−x+1)3.

karton · Accepted Answer

To find the equation of the transformed function, we need to apply the given transformations to the parent function f(x)=x3 in the specified order. Let&#039;s go through each transformation step by step.1. Vertical stretch by a factor of 2.5: We multiply the parent function by 2.5. The equation becomes g(x)=2.5·f(x).2. Reflection over the y-axis: We replace x with −x in the equation. The equation becomes g(x)=2.5·f(−x).3. Horizontal translation left by 1 unit: We add 1 to x in the equation. The equation becomes g(x)=2.5·f(−x+1).Therefore, the equation of the transformed function g(x) is g(x)=2.5·f(−x+1)=2.5·(−x+1)3.

alenahelenash · Accepted Answer

Answer:g(x)=2.5·f(−x−1)=2.5·(−x−1)3Explanation:The parent function is given as f(x)=x3. We need to apply the following transformations to obtain the equation of the transformed function, g(x), in the described order:1. Vertical stretch by a factor of 2.5: To vertically stretch a function, we multiply the function by the stretch factor. Therefore, the first transformation can be written as g(x)=2.5·f(x).2. Reflection over the y-axis: To reflect a function over the y-axis, we replace x with −x. Hence, the equation after the reflection becomes g(x)=2.5·f(−x).3. Horizontal translation left 1 unit: To translate a function horizontally, we add or subtract a value from x. In this case, we translate left 1 unit, so we subtract 1 from x. Thus, the equation after the translation becomes g(x)=2.5·f(−x−1).Combining all the transformations, the equation of the transformed function g(x) is:g(x)=2.5·f(−x−1)=2.5·(−x−1)3

xleb123 · Accepted Answer

Step 1. Vertical stretch by a factor of 2.5: To vertically stretch the function, we multiply the parent function by the stretch factor. The equation becomes:g(x)=2.5·f(x)Substituting the parent function f(x)=x3, we get:g(x)=2.5·x3Step 2. Reflection over the y-axis: To reflect a function over the y-axis, we replace x with -x in the equation. The equation becomes:g(x)=2.5·(−x)3Simplifying the exponent, we have:g(x)=2.5·(−x)3=2.5·(−x·−x·−x)=2.5·(−x3)Step 3. Horizontal translation left 1: To translate a function horizontally, we add the translation value to x. In this case, we&#039;re translating left 1 unit, so we add 1 to x. The equation becomes:g(x)=2.5·(−(x+1))3Combining all the transformations, the final equation of the transformed function g(x) is:g(x)=2.5·(−(x+1))3This equation represents a function obtained by vertically stretching the parent function f(x)=x3 by a factor of 2.5, reflecting it over the y-axis, and horizontally translating it left 1 unit.

Given the parent function f(x) and descriptions of the transformations, write th

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