Chapter 1.3, Problem 3E

In Exercises 1−12, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)−(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window $\left[-4.7,4.7\right]$ by $\left[-3.1,3.1\right]$ .

a. $y=-\sin x$

b. $y=\cos x+1$

c. $y={\left(x+2\right)}^3$

d. $y=e^x-2$

e. $y={\left(x+2\right)}^3$

f. $y=x^3+1$

g. $y=\left|x\right|-2$

h. $y=-1/x$

i. $y=-x$

j. $y=-\sqrt{x}$

k. $y=\mathrm{int}\left(x+1\right)$

l. $y=2-4/\left(1+e^{-x}\right)$

3.

Solution

To match: the given graph with its function and verify with graphing window $\left[-4.7,4.7\right]\times \left[-3.1\times 3.1\right]$ .

The graph matches with option (j) $y=-\sqrt{x}$ .

Given information: The given graph is,

  

Formula used:

The graph of the function $y=-f\left(x\right)$ is found by reflecting the graph of the function $y=f\left(x\right)$ through $x$ -axis.

Calculation:

See the shape of the graph.

The graph resembles to the graph of $y=\sqrt{x}$ .

Consider the basic function $y=\sqrt{x}$ .

Reflect the graph through $x$ -axis.

Thus, the graph of the function is $y=-\sqrt{x}$

The given graph matches with option (j).

Graph the function in the graphing window $\left[-4.7,4.7\right]\times \left[-3.1\times 3.1\right]$, by using graphing calculator:

  

Hence, the graph matches with option (j) $y=-\sqrt{x}$ .