Question

The parent function, $f(x)=5^x$, has been vertically compressed by a factor of one-half, shifted to the right three units and down two units.
Choose the correct function to represent the transformation.

$g(x)=(\frac{1}{2})5^x^-^3-2 \\ \\g(x)=(\frac{1}{2})5^x^+^3-2 \\ \\g(x)=5^{(\frac{1}{2})x-3}-2 \\ \\g(x)=5^{(\frac{1}{2})x+3}-2$

Answer 1

Given: f(x) = 5^x. This is an exponential function.

Vertical compression by a factor of (1/2) results in g(x) = (1/2)5^x.

If this is shifted to the right 3 units, we get h(x) = (1/2)5^(x-3).

Finally, if this is shifted down 2 units, we get k(x) = (1/2)5^(x-3) - 2 (answer)

Answer 2

Answer:

Given: f(x) = 5^x. This is an exponential function.

Vertical compression by a factor of (1/2) results in g(x) = (1/2)5^x.

If this is shifted to the right 3 units, we get h(x) = (1/2)5^(x-3).

if this is shifted down 2 units, we get k(x) = (1/2)5^(x-3) - 2 (answer)

Step-by-step explanation: