Question

The exponential function, f(x)=2^x, undergoes two transformations to g(x)=3x2^x+5. How does the graph change? Select all that apply (choose two)

Answer 1

Answer: Options A and C.

Step-by-step explanation:

 The parent exponential function has the form:

$f(x)=b^x$

This can be transformated as following:

When you multiply the function by a factor a ($a*f(x)$) and a>0 , then the function is  vertically stretched.

When you add a number k to the parent function, the function is shifted up ($f(x)+k$)

The parent function given in the problem is:

$f(x)=2^x$

To obtain the function $g(x)=3*2^x+5$, the parent function is multiplied by a factor 3 (which is greater than 0) and the number 5 is added.

Therefore, the graph is shifted up and vertically stretched.