Question

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the values on both axes range from negative 10 to 10 in increments of 5. a solid curve begins in quadrant 3 sloping upward from left to right. it passes through the origin and then rises through quadrant 1. the solid curve passes through the following: left parenthesis negative 2.1 comma negative 10 right parenthesis, left parenthesis negative 1 comma negative 1 right parenthesis, left parenthesis 1 comma 1 right parenthesis, left parenthesis 2 comma 9 right parenthesis, and left parenthesis 2.1 comma 10 right parenthesis. a dotted curve begins in quadrant 4 sloping upward from left to right. it crosses the x - axis and then rises through quadrant 1. the dotted curve passes through the following: left parenthesis 1.9 comma negative 10 right parenthesis, left parenthesis 3 comma negative 1 right parenthesis, left parenthesis 4 comma 0 right parenthesis, left parenthesis 5 comma 1 right parenthesis, left parenthesis 6 comma 9 right parenthesis, and left parenthesis 6.1 comma 10 right parenthesis. each of the curves is concave down below the x - axis, and concave up above the x - axis. all values are approximate.
analyze the graph of cubic function $f(x)=x^3$ and the transformed function $g(x)$, then determine by how much the graph of $f(x)$ shifts horizontally to the right.
(1 point)
the function $f(x)$ shifts horizontally $\square$ units to the right.
check answer remaining attempts : 3

Explanation:

Step1: Identify key points of \( f(x) = x^3 \)

For \( f(x) = x^3 \), when \( y = -1 \), \( x = -1 \) (since \( (-1)^3 = -1 \)), and when \( y = 1 \), \( x = 1 \) (since \( 1^3 = 1 \)).

Step2: Identify corresponding points of \( g(x) \)

For the transformed function \( g(x) \), when \( y = -1 \), the \( x \)-value is \( 3 \) (from the point \( (3, -1) \)), and when \( y = 1 \), the \( x \)-value is \( 5 \) (from the point \( (5, 1) \)).

Step3: Calculate horizontal shift

To find the horizontal shift, we can use the difference in \( x \)-values for the same \( y \)-value. For \( y = -1 \): shift \( = 3 - (-1) = 4 \). For \( y = 1 \): shift \( = 5 - 1 = 4 \). So the horizontal shift to the right is 4 units.

Answer:

4