Question

23. (04.05)

Which statement best describes the effect of replacing the function f(x) = 2 ^x-2 with the function g(x) = 2 ^x+3

The graph shifts 1 units left.
The graph shifts 5 units left.
The graph shifts 1 unit right.
The graph shifts 3 units right.

Answer 1

The graph shifts 5 units left

Explanation:

The given functions are;

f(x) =
`2^(x - 2)`, g(x) =
`2^(x + 3)`

Therefore, we have;

When x = 2, f(2) =
`2^(2 - 2)` = 1 and g(2) =
`2^(2 + 3)` = 32

When x = 3, f(3) =
`2^(3 - 2)` = 2 and g(3) =
`2^(3 + 3)` = 64

When x = 6, f(6) =
`2^(6 - 2)` = 16 and g(6) =
`2^(6 + 3)` = 512

When x = 7, f(7) =
`2^(7 - 2)` = 32 and g(7) =
`2^(7 + 3)` = 1024

When x = 8, f(8) =
`2^(8 - 2)` = 64 and g(8) =
`2^(8 + 3)` = 2,048

Therefore, the y-value of f(x) obtained at x = 8, is obtained by g(x) at x = 3, and the graph is shifts(ed) 5 units left.