Question

Can anyone help me? Which function is graphed on the right?

Answer 1

Answer:

$y=2^{\left(x-2\right)}+3$

Step-by-step explanation:

To solve this problem, we need to start with the parent function of the exponential function, which is $f(x)=a^x$, where $a$ is the base. In our problem, $a=2$, so our parent function here is $y=2^x$. Then, we need to perform some transformations to our parent function. Thus:

1. Vertical shrink:

A vertical shrink is a nonrigid transformation because the graph of the function get a distortion in the shape, so this transformation is as follows:

$g(x)=cf(x)$

where $c$ in this problem equals 0.25 because:

$y=0.25(2^x) \\ \\ y=\frac{1}{4}(2^x) \\ \\ y=\frac{2^x}{2^2} \\ \\ y=2^{(x-2)}$

2. Vertical shift:

The graph of the function $y=2^{(x-2)}$ get a vertical shift given by:

$y=2^{(x-2)}+3$

So the graph is shifted 3 units up. So the result is the graph shown above.

Answer 2

Answer:

The answer is C

Step-by-step explanation: