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

1. Absolute value function

2. Exponential function

3. Polynomial function (cubic)

4. Cube root function

5. Exponential function

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((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}`