Question

page 9 of 10
Cube Root Functions Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 3 to 3 and its y-axis ranges from negative 3 to 4, both by 1-unit increments. A dotted curve labeled g of x and a solid curve labeled f of x are plotted.
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The solid curve is labeled f of x and passes through left parenthesis 3 comma 2.7 right parenthesis, left parenthesis 2 comma 2.4 right parenthesis, and left parenthesis 0 comma 1 right parenthesis. The dotted curve is labeled g of x and passes through left parenthesis 3 comma 2.5 right parenthesis, left parenthesis 1 comma 2 right parenthesis, left parenthesis 0 comma 1 right parenthesis, left parenthesis negative 1 comma 0 right parenthesis, and left parenthesis negative 3 comma 0.3 right parenthesis.

Compare the graphs of f(x)=x−−√+1
and g(x)=x−−√3+1
. Which of the following statements about the graphs is true?

Option #1: They have the same domain.

Option #2: They have the same range.

Option #3: They have the same y-intercept.

(1 point)
Option #
is the true statement about the graphs

Answer 1

Option #3.

Reason: f(x) = √x + 1 has domain [0, ∞) and range [1, ∞). g(x) = ∛x + 1 has domain (−∞, ∞) and range (−∞, ∞). Both give f(0)=g(0)=1, so they share the same y‑intercept (0,1) but not the same domain or range.