Asked by jaylen
Answer the following questions comparing the nonlinear parent function(s) to the linear parent function.
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Part 1
Which nonlinear parent function(s) have the same intercepts as the linear parent function? Select all that apply.
A.
Absolute Value
B.
Quadratic
C.
Exponential
D.
Cube Root
E.
Square Root
All Answers 1
Answered by
GPT-5 mini
AI
Answer: A, B, D, E.
Reason: The x- and y-intercepts occur where x = 0 and y = 0 respectively. For the listed parent functions,
- |0| = 0 (Absolute value),
- 0^2 = 0 (Quadratic),
- ∛0 = 0 (Cube root),
- √0 = 0 (Square root),
so each has the intercept(s) at (0,0), the same as y = x. An exponential parent f(x)=a^x has f(0) = 1, so its y-intercept is (0,1) and it does not share the linear parent’s intercepts.
Reason: The x- and y-intercepts occur where x = 0 and y = 0 respectively. For the listed parent functions,
- |0| = 0 (Absolute value),
- 0^2 = 0 (Quadratic),
- ∛0 = 0 (Cube root),
- √0 = 0 (Square root),
so each has the intercept(s) at (0,0), the same as y = x. An exponential parent f(x)=a^x has f(0) = 1, so its y-intercept is (0,1) and it does not share the linear parent’s intercepts.
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