Question

The exponential function, f(x) = 2^x, undergoes two transformations to g(x) = 1/3 x 2^x - 7. how does the graph change? select all that apply. A. It is vertically compressed. B. It is vertically stretched. C. It is shifted right. D. It is shifted down E. It is lipped over the x-axis.

Answer 1

A and D

Explanation:

Since a (1/3) is less than 1, it is vertically compressed. The -7 is outside of the parenthesis so it is shifting down.

Answer 2

options A and D are the correct options.

Explanation:

The parent exponential function is f(x) = 2ˣ

Now this function undergoes two transformations to form g(x) =
`(1)/(3)(2^(x))-7`

When parent function f(x) = 2ˣ is multiplied by
`(1)/(3)`, this means f(x) has been compressed vertically because
`(1)/(3)` < 1.

Now we subtract 7 from the new function
`(1)/(3)`
`(2^(x))`, that means we are shifting this function 7 units downwards on y-axis.

Therefore, options A and D are the correct options.