Question

if $f(x)=7^x$ is horizontally stretched by a factor of 5, moved up 3 units, and reflected across the x-axis, which of the following is the new expression of $f(x)$? (5 points)○ $f(x)=-7^{5x}+3$○ $f(x)=-7^{\frac{1}{5}x}+3$○ $f(x)=\frac{1}{5}\cdot7^{-x}+3$○ $f(x)=-5\cdot7^x+3$

Explanation:

Step1: Horizontal stretch by 5

Replace $x$ with $\frac{1}{5}x$: $f(x) = 7^{\frac{1}{5}x}$

Step2: Shift up 3 units

Add 3 to the function: $f(x) = 7^{\frac{1}{5}x} + 3$

Step3: Reflect across x-axis

Multiply the function by $-1$: $f(x) = -7^{\frac{1}{5}x} + 3$

Answer:

$f(x) = -7^{\frac{1}{5}x} + 3$