Question

classify each function into its function family based on the characteristics ovserved for the parent function (only need help on the 2nd and third question, but if i got the other ones wrong i would apprecaute if someone told me

Answer 1

Answer:

1.  Absolute value function

2.  Exponential function

3.  Polynomial function (cubic)

4.  Cube root function

5.  Exponential function

Step-by-step explanation:

Absolute Value Function

An equation that contains an algebraic expression within absolute value symbols.

$\textsf{e.g.}\quad y = |x + 9|$

Exponential Function

$y=ab^x$

The variable is the exponent.

A continuous function with a horizontal asymptote.

An exponential function has a fast growth or decay.

$\textsf{e.g.}\quad y =-\left(\dfrac{1}{2}\right)^x$

Polynomial Function

$y=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0$

An equation containing variables with non-negative integer powers and coefficients, that involves only the operations of addition, subtraction and multiplication.

$\textsf{e.g.}\quad y = x^3 - 6$

Cube Root Function

The inverse function of the cubic function.

A reflection of the cubic function in the line y = x.

$\textsf{e.g.}\quad y=\sqrt[3]{x}$