Question

question 3 0.5 pts match the following special types of lines to the corresponding slope. vertical line choose choose m = 0 horizontal line m = undefined question 4 0.5 pts what is the parent function of the equation y = 2x³ + 5x - 1 absolute value

Explanation:

Question 3

Step1: Recall slope of vertical line

A vertical line has an undefined slope because the change in \(x\) (run) is \(0\), and slope \(m=\frac{\text{rise}}{\text{run}}\), division by zero is undefined. So Vertical Line: \(m=\text{undefined}\).

Step2: Recall slope of horizontal line

A horizontal line has a slope of \(0\) because the change in \(y\) (rise) is \(0\), so \(m = \frac{0}{\text{run}}=0\) (where run is non - zero). So Horizontal Line: \(m = 0\).

The parent function is the simplest form of a function in a family of functions. The given function \(y = 2x^{3}+5x - 1\) is a cubic function. The simplest cubic function (parent function) is \(y=x^{3}\), as the given function is a transformation (scaling, and addition of linear and constant terms) of the basic cubic function \(y = x^{3}\).

Answer:

Vertical Line: \(m=\text{undefined}\)
Horizontal Line: \(m = 0\)

Question 4