Question

question 7
1 pts
identify the parent function of each. if there is more than one, type answer in with no capitalization, for example: linear
a.
b.
c.
d.
e.
f.
a
b
c
d
e
f

Answer:

To solve this, we analyze each graph:

Part A

The graph is a polynomial with a "W" or even - degree polynomial shape, typical of a quartic (degree 4) or a transformed polynomial, but the parent function here, looking at the symmetry and shape, the parent function is a polynomial (specifically, the parent could be \( y = x^4 \) or a general polynomial, but the base parent for such a curved, symmetric (about y - axis in a transformed way) polynomial - like graph is a polynomial. But more precisely, the shape is similar to a quartic, but the parent function here, considering the general polynomial family, the parent function is a polynomial (if we consider the basic polynomial functions, the parent for a curve like this with multiple turning points is a higher - degree polynomial, but the most appropriate parent function here is a polynomial (specifically, the parent could be \( y=x^4 \), but the answer is "polynomial" or more precisely "quartic" but as per the example, we can say "polynomial" or more accurately, the parent function is a quartic (degree 4) polynomial, but the base parent function here is a polynomial. However, the most common parent function for such a symmetric, curved graph with two "humps" on the sides and a minimum in the middle (after transformation) is the quartic function \( y = x^4 \), but the answer should be in the form like the example. So the parent function is "polynomial" (or more precisely "quartic").

Part B

The graph has an exponential growth shape. The parent function for exponential growth is \( y = a^x \) (\( a>1 \)). So the parent function is "exponential".

Part C

The graph has a cubic - like shape (with a local maximum and a local minimum, and the ends going in opposite directions). The parent function for a cubic function is \( y=x^3 \). So the parent function is "cubic" (or "polynomial - cubic").

Part D

The graph is a parabola opening upwards, which is the shape of a quadratic function. The parent function for a quadratic function is \( y = x^2 \). So the parent function is "quadratic".

Part E

The graph has a combination of a linear (the left - hand "V" - like part) and a quadratic (the right - hand parabola - like part), but overall, the right - hand part is a quadratic and the left - hand part is a linear, but the parent functions here are "linear" and "quadratic", but the overall graph is a piece - wise function with a linear and a quadratic part. However, the parent functions for the two parts: the left part is a linear function (\( y = |x| \) - like? No, the left part is a line, and the right part is a parabola. Wait, the left part is a line (linear) and the right part is a quadratic (\( y=x^2 \)). But the parent functions here are "linear" (for the left - hand line) and "quadratic" (for the right - hand parabola). But the question says "parent function of each", so for the right - hand part, the parent is "quadratic" and for the left - hand part, the parent is "linear".

Part F

The graph is a "V" - shaped graph, which is the shape of an absolute value function. The parent function for the absolute value function is \( y = |x| \). So the parent function is "absolute value".

Final Answers

A. polynomial (or quartic)
B. exponential
C. cubic
D. quadratic
E. piece - wise (with linear and quadratic parents) but for the right - hand quadratic part, parent is "quadratic" and left - hand linear part, parent is "linear"
F. absolute value

(Note: The answers are based on the shape of each graph and the definition of parent functions. Parent functions are the basic functions from which other functions are derived through transformations like shifting, stretching, compressing, or reflecting.)

If we follow the example (like "linear" in the example), the answers are:

A. polynomial
B. exponential
C. cubic
D. quadratic
E. piece - wise (linear and quadratic)
F. absolute value

But to match the example's style (e.g., "linear"), we can write:

A. polynomial
B. exponential
C. cubic
D. quadratic
E. quadratic (for the right - hand part) / linear (for the left - hand part)
F. absolute value

However, if we strictly follow the example (single - word or short - phrase answers):

A. polynomial
B. exponential
C. cubic
D. quadratic
E. quadratic (for the parabola part)
F. absolute value

The most appropriate answers for each part:

A. polynomial
B. exponential
C. cubic
D. quadratic
E. quadratic (right part) / linear (left part)
F. absolute value

But if we consider the main parent function for each graph:

A. Polynomial (specifically quartic)
B. Exponential
C. Cubic
D. Quadratic
E. Quadratic (for the parabolic part)
F. Absolute Value

So, for each sub - part:

A. \(\boldsymbol{\text{polynomial}}\)
B. \(\boldsymbol{\text{exponential}}\)
C. \(\boldsymbol{\text{cubic}}\)
D. \(\boldsymbol{\text{quadratic}}\)
E. \(\boldsymbol{\text{quadratic}}\) (for the right - hand parabolic segment)
F. \(\boldsymbol{\text{absolute value}}\)

(The answers are determined by the shape of each graph and the definition of parent functions in algebra. Parent functions are the simplest form of a function type, from which more complex functions are created by applying transformations.)