Chapter 4, Problem 1PRE

(a)

To determine

To calculate: The domain of the function $f\left(x\right)=3$.

Answer to Problem 1PRE

Solution:

The domain of the function is $\underset{\_}{\left(-\infty ,\infty \right)}$.

Explanation of Solution

Given:

The function, $f\left(x\right)=3$.

Calculation:

The domain is the all possible input for any provided function.

$f\left(x\right)=3$.

Here, the domain will be $\left(-\infty ,\infty \right)$.

(b)

To determine

The range of the function $f\left(x\right)=3$.

Answer to Problem 1PRE

Solution: The range is $\underset{\_}{\left\{3\right\}}$

Explanation of Solution

Given: $f\left(x\right)=3$

The range is all the possible outputs of a given function,

Here, for $f\left(x\right)=3$, the output is constant for any value of x,

Hence, the range is $\left\{3\right\}$

(c)

To determine

The x-intercept(s) of the function $f\left(x\right)=3$.

Answer to Problem 1PRE

Solution: There is no x-intercept.

Explanation of Solution

Given: $f\left(x\right)=3$

To find the x-intercept(s), solve the equation $f\left(x\right)=0$,

$f\left(x\right)=3$

$0=3$

This is false,

Hence, there is no x-intercept.

(d)

To determine

The y-intercept(s) of the function $f\left(x\right)=3$.

Answer to Problem 1PRE

Solution: The y-intercept is $\underset{\_}{(0,3})$.

Explanation of Solution

Given: $f\left(x\right)=3$

To find the y-intercept(s), evaluate $f\left(0\right)$,

$f\left(0\right)=3$

The y-intercept is 3.

(e)

To determine

The asymptotes if applicable for the function $f\left(x\right)=3$..

Answer to Problem 1PRE

Solution: No asymptotes.

Explanation of Solution

Given: $f\left(x\right)=3$

Since the given function is a constant function, i.e., no curve involved.

Hence, no asymptotes.

(f)

To determine

The intervals over which the function $f\left(x\right)=3$ is increasing.

Answer to Problem 1PRE

Solution: Never increasing.

Explanation of Solution

Given: $f\left(x\right)=3$

Since the given function is a constant function, i.e., no curve involved.

Hence, never increasing.

(g)

To determine

The intervals over which the function $f\left(x\right)=3$ is decreasing.

Answer to Problem 1PRE

Solution: Never decreasing.

Explanation of Solution

Given: $f\left(x\right)=3$

A function is an increasing function if the function values increase within the given interval. Similarly, a function is a decreasing function if the function values decrease within the given interval.

Since the given function is a constant function, i.e., no curve involved.

Hence, the given function $f\left(x\right)=3$ is never decreasing.

(h)

To determine

The match of the function $f\left(x\right)=3$ with its graph.

Answer to Problem 1PRE

Solution: Graph E.

Explanation of Solution

Given: $f\left(x\right)=3$

Since the given function is a constant function where for any value of x the output is 3,

Hence the graph will be a horizontal straight line crossing the y-axis at $+3$.

The correct match will be graph E