Questions: Describe verbally the transformations that can be used to obtain the graph of g from the graph of f. g(x) = 7^(x+8) ; f(x) = 7^x Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Type integers or simplified fractions.) A. The graph of g is the graph of f shifted unit(s) to the left and stretched horizontally by a factor of . B. The graph of g is the graph of f reflected in the y-axis. C. The graph of g is the graph of f reflected in the x-axis. D. The graph of g is the graph of f shifted unit(s) to the right. E. The graph of g is the graph of f shifted unit(s) up. F. The graph of g is the graph of f shifted unit(s) to the left. G. The graph of g is the graph of f shifted unit(s) down. H. The graph of g is the graph of f shifted unit(s) down and stretched horizontally by a factor of . I. The graph of g is the graph of f shifted unit(s) up and stretched horizontally by a factor of . J. The graph of g is the graph of f shifted unit(s) to the right and stretched horizontally by a factor of .

Describe verbally the transformations that can be used to obtain the graph of g from the graph of f. g(x) = 7^(x+8) ; f(x) = 7^x Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Type integers or simplified fractions.) A. The graph of g is the graph of f shifted unit(s) to the left and stretched horizontally by a factor of . B. The graph of g is the graph of f reflected in the y-axis. C. The graph of g is the graph of f reflected in the x-axis. D. The graph of g is the graph of f shifted unit(s) to the right. E. The graph of g is the graph of f shifted unit(s) up. F. The graph of g is the graph of f shifted unit(s) to the left. G. The graph of g is the graph of f shifted unit(s) down. H. The graph of g is the graph of f shifted unit(s) down and stretched horizontally by a factor of . I. The graph of g is the graph of f shifted unit(s) up and stretched horizontally by a factor of . J. The graph of g is the graph of f shifted unit(s) to the right and stretched horizontally by a factor of .
Transcript text: Describe verbally the transformations that can be used to obtain the graph of $g$ from the graph of $f$. \[ g(x)=7^{x+8} ; f(x)=7^{x} \] Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Type integers or simplified fractions.) A. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) to the left and stretched horizontally by a factor of $\square$ . B. The graph of $g$ is the graph of $f$ reflected in the $y$-axis. C. The graph of $g$ is the graph of $f$ reflected in the $x$-axis. D. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) to the right. E. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) up. F. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) to the left. G. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) down. H. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) down and stretched horizontally by a factor of $\square$ . I. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) up and stretched horizontally by a factor of $\square$ . J. The graph of $g$ is the graph of $f$ shifted $\square$ unit(s) to the right and stretched horizontally by a factor of $\square$ .
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Solution

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Solution Steps

To transform the graph of \( f(x) = 7^x \) into the graph of \( g(x) = 7^{x+8} \), we need to identify the effect of the transformation \( x \to x+8 \). This transformation shifts the graph horizontally. Specifically, adding 8 to the input \( x \) shifts the graph 8 units to the left.

Solution Approach
  • Identify the transformation in the function \( g(x) = 7^{x+8} \) compared to \( f(x) = 7^x \).
  • Recognize that adding a constant to \( x \) results in a horizontal shift.
  • Determine the direction and magnitude of the shift.
Step 1: Identify the Transformation

The function \( g(x) = 7^{x+8} \) can be compared to \( f(x) = 7^x \). The transformation involves the expression \( x + 8 \), indicating a shift in the graph.

Step 2: Determine the Direction and Magnitude of the Shift

The addition of 8 to \( x \) signifies that the graph of \( f(x) \) is shifted horizontally. Specifically, since we are adding to \( x \), the graph shifts to the left by 8 units.

Final Answer

The graph of \( g \) is the graph of \( f \) shifted \( 8 \) units to the left. Thus, the answer is A.

\(\boxed{A}\)

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