Q. 54 - Precalculus Enhanced with Graphing Utilities

Question

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) $G\left(x\right)=-\frac{2}{3}x+3$

Step-by-Step Solution

Answer

Part (a) The graph could not be of function.

Part (b) The graph could be of function.

Part (c) The graph could not be of function.

Part (d) The graph could not be of function.

Part (e) The graph could be of function.

Part (a) Step 1. Given information

The graph is given, Check function for given graph.

Part (a) Step 2. Explanation.

The function is $f\left(x\right)=3x+1$.

Here, y-intercept is 1 and slope is 3.

As slope is positive, so the function is increasing but the given graph is decreasing so graph could not be of function.  

Part (b) Step 1. Explanation.

The function is $f\left(x\right)=-2x+3$ .

Here, y-intercept is 3 and slope is -2.

As slope is negative, so the function is decreasing and the given graph is decreasing so graph could be of function.  

Part (c) Step 1. Explanation.

The function is $H\left(x\right)=3$.

This is constant function. the graph of this function is parallel to x-axis.

The given graph could not of this function. 

Part (d) Step 1. Explanation.

The function is $F\left(x\right)=-4x-1$.

Here, y-intercept is -1 and slope is -4.

As slope is negative, so the function is decreasing and the given graph is decreasing but y-intercept is positive in the graph. So, graph could be of this function.  

Part (e) Step 1. Explanation.

The function is $G\left(x\right)=-\frac{2}{3}x+3$.

Here, y-intercept is 3 and slope is $-\frac{2}{3}$.

As slope is negative, so the function is decreasing and the given graph is also decreasing. so graph could be of this function.