# Function Worksheets - Page 4

Function Worksheets
• Page 4
31.
Find the domain of the function $f$($x$) = .
 a. (- ∞, 7] b. (- ∞, 7) c. (- ∞, ∞) d. [7, ∞)

#### Solution:

f(x) = 7 - x

In order to have f(x) = 7 - x as a real number, we must have 7 - x ≥ 0 or x ≤ 7. Thus the domain of f(x) is [7, ∞)

32.
Find the domain of the function $f$($x$) =
 a. (- ∞, 2) b. (- ∞, ∞) c. (2, ∞) d. (- ∞, 2]

#### Solution:

f(x) = 12 - x

In order to have f(x) = 12 - x as a real number we must have 2 - x > 0 or x < 2

So, the domain of f( x) is D = (- ∞, 2)

33.
Find the domain of the function $f$($x$) = .
 a. (- ∞, ∞) b. (4, 8) c. (- ∞, 8) $\cup$ (8, ∞) d. (- ∞, 4] $\cup$ [8, ∞)

#### Solution:

f(x) = x2 - 12x + 32 = (x - 4 )(x - 8)

In order to have f(x) = x2 - 12x + 32 = (x - 4)(x - 8) as a real number we must have (x - 4) (x - 8) ≥ 0

x (- ∞, 4] [8, ∞)
[Solve the inequality.]

So, the domain of f(x) = D = (- ∞, 4] [8, ∞)

34.
Find the domain of the function $f$($x$) = .
 a. (- ∞, 3) $\cup$ (8, ∞) b. (- ∞, 8) c. (- ∞, 3] d. [8, ∞)

#### Solution:

f(x) = 1x2 - 11x + 24 = 1(x - 8)(x - 3)

In order to have f(x) = 1(x - 8)(x - 3) as a real number, we must have (x - 8)(x - 3) > 0

x (- ∞, 3) (8, ∞)
[Solve the inequality.]

So, the domain of f(x) = (- ∞, 3) (8, ∞)

35.
Find the domain of the function $f$($x$) =.
 a. [6, 7) b. (6, 7] c. (- ∞, ∞) d. [6, 7]

#### Solution:

f(x) = 6 - xx - 7

In order to have f(x) = 6 - xx - 7 as a real number we must have 6 - xx - 7 ≥ 0 or (6 - x) (x - 7) ≥ 0 and x ≠ 7

(x - 6) (x - 7) ≤ 0 and x ≠ 7

x [6, 7)
[Solve the inequality.]

36.
Which of the following is the largest domain of the function $f$($x$) = $\sqrt{{x}^{2}}$ + 2?
 a. (- ∞, ∞) b. (- 2, 2) c. (2, ∞) d. (- ∞, 2)

#### Solution:

f(x) = x2 + 2

= |x| + 2
[Use x2 = |x|.]

Since |x| + 2 is a real number for every real x, the domain of f(x) = D = (- ∞, ∞)

37.
Find the domain of the function $f$($x$) = .
 a. (- ∞, 3] b. (- ∞, ∞) c. (- ∞, 3) $\cup$ (3, ∞) d. [3, ∞)

#### Solution:

f(x) = x2 - 9x - 3

The function f(x) is not defined at x = 3.

So, the domain of f(x) is all real numbers except 3

That is the domain of the function f(x) in the intervel notation is (- ∞, 3) (3, ∞)

38.
The graph of the function rule intersect the $y$-axis at (0, 13). Which of the following is true about the coordinates of the point?
 a. Input = 13, Output = 13 b. Input = 0, Output = 13 c. Input = 13, Output = 0 d. Input = 0, Output = 0

#### Solution:

The graph of the function rule intersect the y-axis at (0, 13) means the function output is 13 for an input of 0.

39.
Objective : Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities including representations involving computer algebra systems, spreadsheets, and graphing calculators.
Which table describe the function $f$($x$) = - 2$x$ + 1, if $x$ = 0, 1, 2, 3?

 a. Table - 1 b. Table - 2 c. Table - 4 d. Table - 3

 $x$ 0 2 4 8 $y$ 2 3 4 6
 a. $y$ = 2$x$ - 1 b. $y$ = $x$ + 2 c. $y$ = $\frac{1}{2}$$x$ + 2 d. $y$ = 2($x$ - 1)