Chapter 3.1, Problem 54AYU

Which of the following functions might have the graph shown? More than one answer is possible).

a. $f\left(x\right)= 3x+1$

b. $g\left(x\right)=-2x+3$

c. $H\left(x\right)=3$

d. $F\left(x\right)= -4x–1$

e. $G(x)= -\frac{2}{3}x+3$

To determine

We have to determine which of the given function might have the graph shown.

Answer to Problem 54AYU

Solution:

b. $g(x)=-2x+3$

Or

d. $G(x)=-\frac{2}{3}x+3$

Explanation of Solution

Given:

The given graph is

a. $f(x)=3x+1$

b. $g(x)=-2x+3$

c. $H(x)=3$

d. $F(x)=-4x-1$

e. $G(x)=-\frac{2}{3}x+3$

We know that a linear function is of the general form $f(x)=mx+c$, where $m$ is the slope of the given function and $c$ is the $y\text{-intercept}$ which is the original value of the function when $x=0$.

Equation of a vertical line is $x=b$, where $b$ is any constant.

Equation of a horizontal line is $f(x)=c$.

From the given graph, we can see that it has a negative slope and is not a horizontal or a vertical line.

We can also notice that the $y\text{-intercept}$ of the graph is a positive number.

Therefore, from the given functions (a., (c. and (d. can be eliminated.

Thus, the linear function of this graph can either be functions

b. $g(x)=-2x+3$

Or

d. $G(x)=-\frac{2}{3}x+3$