Chapter 1.1, Problem 54E

a.

To determine

To substitute: The correct number from the given numbers so that the graph intersects the $x-axis$ .

Answer to Problem 54E

The function is $f(x)=3x^1+1$.

Explanation of Solution

Given Information: Function is $f(x)=3x^{?}+1$ .

  $1$ can be placed in the empty box so that the function becomes $f(x)=3x^1+1$ . Now, the function is linear, it will intersect the $x-axis$ .

Thus, the function is $f(x)=3x^1+1$.

b.

To determine

To substitute: The correct number from the given numbers so that the graph intersects the $x-axis$ .

Answer to Problem 54E

The function is $f(x)=\left|2x-6\right|-2$.

Explanation of Solution

Given Information: Function is $f(x)=\left|2x-6\right|-?$ .

  $2$ can be placed in the empty box so that the function becomes $f(x)=\left|2x-6\right|-2$ . It is vertically translated down $2units$ , it intersects $x-axis$ .

Thus, the function is $f(x)=\left|2x-6\right|-2$.

c.

To determine

To substitute: The correct number from the given numbers so that the graph intersects the $x-axis$ .

Answer to Problem 54E

The function is $f(x)=-x^2+1$

Explanation of Solution

Given Information: Function is $f(x)=?(x^2)+1$ .

Calculation:

  $-1$ can be placed in the empty box so that the function becomes $f(x)=-x^2+1$ . This way it is reflected over the $x-axis$ and then shifted up. Now, the function intersects $x-axis$ .

Thus, the function is $f(x)=-x^2+1$ .

d.

To determine

To substitute: The correct number from the given numbers so that the graph intersects the $x-axis$ .

Answer to Problem 54E

The function is $f(x)=0$ .

Explanation of Solution

Given Information: Function is $f(x)=?$ .

  $0$ can be placed in the empty box so that the function becomes constant $f(x)=0$ . All its points now lie on $x-axis$ .

Thus, the function is $f(x)=0$ .