QuestionStarting with the graph of $f(x)=5^{x}$ , write the equation of the graph that results from (a) shifting $f(x) 7$ units downward. $y=5^{x}-7$ $\square$ $0^{8}$ (b) shifting $f(x) 4$ units to the left. $y=$ $\square$ $5^{x+4}$ $0^{6}$ $\square$

Studdy Solution

STEP 1

1. The function $f(x) = 5^x$ is an exponential function.
2. Transformations include vertical shifts and horizontal shifts.
3. The transformations are applied to the function $f(x)$ .

STEP 2

1. Apply a vertical shift to the function $f(x)$ .
2. Apply a horizontal shift to the function $f(x)$ .

STEP 3

To shift the graph of $f(x) = 5^x$ 7 units downward, subtract 7 from the function:
$y = 5^x - 7$

STEP 4

To shift the graph of $f(x) = 5^x$ 4 units to the left, replace $x$ with $x + 4$ in the function:
$y = 5^{x+4}$
The equations for the transformed graphs are: (a) $y = 5^x - 7$ (b) $y = 5^{x+4}$

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