Chapter 3.1, Problem 53AYU

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

a. $f\left(x\right)=2x-7$

b. $g(x) =-3x+4$

c. $H\left(x\right)=5$

d. $F(x)=3x+4$

e. $G\left(x\right)= x+2$

To determine

Which of the given function might have the graph shown:

a. $f(x)=2x-7$

b. $g(x)=-3x+4$

c. $H(x)=5$

d. $F(x)=3x+4$

e. $G(x)=\frac{1}{2}x+2$

Answer to Problem 53AYU

Solution:

d. $F(x)=3x+4$

Or

e. $G(x)=\frac{1}{2}x+2$

Explanation of Solution

Given:

The given graph is

Calculation:

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., (b. and (c. can be eliminated.

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

d. $F(x)=3x+4$

Or

e. $G(x)=\frac{1}{2}x+2$