Questions: Section 2.4 2.5= Question 1, 2.5.13 Part 1 of 2 Describe how the given function can be obtained from one of the basic graphs. Then graph the function. g(x)=-(x-4)^3 A. Start with the graph of f(x)= the x-axis. B. Start with the graph of f(x)= Shift it right 4 units and then reflect it across the y-axis. C. Start with the graph of f(x)= Shift it left 4 units and then reflect it across the y-axis. D. Start with the graph of f(x)= Shift it right 4 units and then reflect it across the x-axis.

Section 2.4 2.5= Question 1, 2.5.13 Part 1 of 2 Describe how the given function can be obtained from one of the basic graphs. Then graph the function. g(x)=-(x-4)^3 A. Start with the graph of f(x)= the x-axis. B. Start with the graph of f(x)= Shift it right 4 units and then reflect it across the y-axis. C. Start with the graph of f(x)= Shift it left 4 units and then reflect it across the y-axis. D. Start with the graph of f(x)= Shift it right 4 units and then reflect it across the x-axis.
Transcript text: Section $2.4 \& 2.5=$ Question 1, 2.5.13 Part 1 of 2 Describe how the given function can be obtained from one of the basic graphs. Then graph the function. \[ g(x)=-(x-4)^{3} \] A. Start with the graph of $f(x)=$ $\qquad$ the $x$-axis. B. Start with the graph of $f(x)=$ $\square$ Shift it right 4 units and then reflect it across the $y$-axis. C. Start with the graph of $f(x)=$ $\square$ Shift it left 4 units and then reflect it across the $y$-axis. D. Start with the graph of $f(x)=$ $\square$ Shift it right 4 units and then reflect it across the $x$-axis.
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Solution

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Solution Steps

Step 1: Identify the Basic Graph

The given function is \( g(x) = -(x-4)^3 \). The basic graph to start with is \( f(x) = x^3 \).

Step 2: Apply Transformations
  1. Shift Right 4 Units: The transformation \( f(x-4) = (x-4)^3 \) shifts the graph of \( f(x) = x^3 \) to the right by 4 units.
  2. Reflect Across the X-axis: The transformation \( g(x) = -(x-4)^3 \) reflects the graph across the x-axis.

Final Answer

The function \( g(x) = -(x-4)^3 \) is obtained by starting with the graph of \( f(x) = x^3 \), shifting it right 4 units, and then reflecting it across the x-axis.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = -(x-4)**3"], "latex_expressions": ["$y = -(x-4)^3$"]}

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