Question

Compare the graphs of f(x)=√x and g(x)=3√x. Which of the following options is true? (1 point)
Responses

Both functions have the same domain, [0,∞)
.
Both functions have the same domain, left bracket 0 comma infinity right parenthesis .

Both functions have the same range, (−∞,∞)
.
Both functions have the same range, left parenthesis negative infinity comma infinity right parenthesis .

Both functions are increasing.
Both functions are increasing.

Both functions go through the point (−1,−1)
.
Both functions go through the point left parenthesis negative 1 comma negative 1 right parenthesis .

Answer 1

True:
- Both functions have the same domain, [0, ∞). (√x is defined only for x ≥ 0, and multiplying by 3 does not change the domain.)
- Both functions are increasing on their domain. (For x ≥ 0, √x and 3√x both increase as x increases.)

False:
- They do not have range (−∞, ∞). Their ranges are [0, ∞).
- They do not go through (−1, −1) because x = −1 is not in their domain.