Which equation is the parent function of an exponential equation?

A. y = x²

B. y = a^x

C. y = |x|

D. y equals one divided by x y = 1 x

A
Incorrect. This is the quadratic parent function.

B
Correct! This is the exponential parent function.

C
Incorrect. This is the absolute value parent function.

D
Incorrect. This is the reciprocal parent function.

Which is the best representation of the function y = |x|?

A
Incorrect. This is a linear function (but not the linear parent function.)

B
Correct! This is the absolute value parent function.

C
Incorrect. This is the linear parent function.

D
Incorrect. This is the quadratic parent function.

Which graph below represents the parent function of a quadratic function?

A
Incorrect. The vertex of the quadratic parent function must be at the origin, (0, 0), and the vertex of this quadratic function is at (-1, 0).

B
Incorrect. The vertex of the quadratic parent function must be at the origin, (0, 0), and the vertex of this quadratic function is at (0, 1).

C
Incorrect. This parabola is open wider than the quadratic parent function. If you compare a table of values for this function and a table of values for the quadratic parent function, you will see that this function has been transformed.

D
Correct! This is the quadratic parent function!

Which of the following are characteristics of the quadratic parent?

I. The parent function of a quadratic equation has its vertex at (0, 0).

II. The parent function of a quadratic equation opens upward.

III. The parent function of a quadratic equation has the x-axis as its axis of symmetry.

A. I and II only
Correct! The vertex of the quadratic parent function must be at the origin, (0, 0), and the parabola opens upward.

B. I and III only
Incorrect. While it is true that the vertex of the quadratic parent function must be at the origin, (0, 0), Part III is not true because a quadratic parent function has the y-axis as its axis of symmetry.

C. II and III only
Incorrect. While it is true that the graph of the quadratic parent function opens upward, Part III is not true because a quadratic parent function has the y-axis as its axis of symmetry.

D. I, II, and III
Incorrect. While it is true that the vertex of the quadratic parent function must be at the origin, (0, 0), and the graph of the quadratic parent function opens upward, Part III is not true because a quadratic parent function has the y-axis as its axis of symmetry.

Which type of parent function is represented by the function graphed below?

A. Exponential
Incorrect. This is what the exponential parent graph looks like.

B. Square Root Function
Incorrect. This is what the square root parent graph looks like.

C. Logarithmic Function
Correct! The graph is the graph of the logarithmic parent function.

D. Linear Function
Incorrect.