Question 1

Write the domain in interval notation.
-$$f ( x ) = \frac { 4 } { \sqrt { 3 - x } }$$
A) $( - \infty , 3 )$
B) $( 3 , \infty )$
C) $( - \infty , 3 ]$
D) $[ 3 , \infty )$

Accepted Answer

The domain of $f(x) = \frac{4}{\sqrt{3-x}}$ consists of all real numbers $x$ for which the expression under the square root, $3-x$, is positive. This is because the square root of a negative number is not defined in the set of real numbers. Therefore, $3-x > 0$, which simplifies to $x < 3$. This means the function is defined for all $x$ less than 3, which is represented by the interval $(- \infty , 3)$.

Question 2

Write the domain in interval notation.
-$$h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$$
A) $( - 11 , - 10 ) \cup ( - 10 , \infty )$
B) $[ - 11 , - 10 ) \cup ( - 10 , \infty )$
C) $( - 11 , \infty )$
D) $[ - 11 , \infty )$

Accepted Answer

The answer of Write the domain in interval notation.
-\[h (...

Question 3

Write the domain in interval notation.
-$$w ( a ) = \frac { 4 } { 6 - | a - 3 | }$$
A) $( - \infty , 9 ) \cup ( 9 , \infty )$
B) $( - \infty , \infty )$
C) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
D) $( - \infty , - 3 ) \cup ( - 3,9 ) \cup ( 9 , \infty )$

Accepted Answer

The answer of Write the domain in interval notation.
-\[w (...

Question 4

Determine the domain and range of the function.
-
A) Domain: $( - \infty , \infty )$; Range $( - \infty , 1 ]$
B) Domain: $( - \infty , 1 ]$; Range $( - \infty , \infty )$
C) Domain: $( - \infty , \infty )$; Range $( - \infty , \infty )$
D) Domain: $( - \infty , 1 ]$; Range $[ 3 , \infty )$

Accepted Answer

The answer of Determine the domain and range of the...

Question 5

Write the domain in interval notation.
-$$p ( x ) = 7 x + 1 ; x \geq 0$$
A) $\left( - \infty , - \frac { 1 } { 7 } \right) \cup \left( - \frac { 1 } { 7 } , \infty \right)$
B) $( - \infty , \infty )$
C) $[ 0,4 )$
D) $[ 0 , \infty )$

Accepted Answer

The domain of $p(x) = 7x + 1$ given $x \geq 0$ is all non-negative real numbers, which is represented by $[0, \infty)$.

Question 6

Determine the domain and range of the function.
-
A) Domain: $[ 2 , \infty )$; Range: $( - \infty , \infty )$
B) Domain: $( - \infty , \infty )$; Range: $( - \infty , 2 ]$
C) Domain: $( - \infty , \infty )$; Range: $[ 2 , \infty )$
D) Domain: $( - \infty , 2 ]$; Range: $( - \infty , \infty )$

Accepted Answer

The answer of Determine the domain and range of the...

Question 7

Write the domain in interval notation.
-$$f ( x ) = \frac { x + 7 } { x + 3 }$$
A) $( - \infty , 3 ) \cup ( 3 , \infty )$
B) $( - \infty , 7 ) \cup ( 7 , \infty )$
C) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
D) $( - \infty , - 7 ) \cup ( - 7 , \infty )$

Accepted Answer

The domain of the function excludes the value that makes the denominator zero, which is $x = -3$, hence the correct domain is $( - \infty , - 3 ) \cup ( - 3 , \infty )$.

Question 8

Write the domain in interval notation.
-$$k ( x ) = \frac { x + 9 } { x - 4 }$$
A) $( - \infty , 9 ) \cup ( 9 , \infty )$
B) $( - \infty , - 4 ) \cup ( - 4 , \infty )$
C) $( - \infty , 4 ) \cup ( 4 , \infty )$
D) $( - \infty , - 9 ) \cup ( - 9 , \infty )$

Accepted Answer

The answer of Write the domain in interval notation.
-\[k (...

Question 9

Write the domain in interval notation.
-$$m ( x ) = \frac { 5 } { | x | + 1 }$$
A) $( - \infty , - 5 ) \cup ( - 5 , \infty )$
B) $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$
C) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
D) $( \infty , \infty )$

Accepted Answer

The answer of Write the domain in interval notation.
-\[m (...

Question 10

Write the domain in interval notation.
-$$r ( x ) = x ^ { 2 } + 2 x - 35$$
A) $( - \infty , - 8 ) \cup ( - 8 , \infty )$
B) $( - \infty , - 7 ) \cup ( - 7,5 ) \cup ( 5 , \infty )$
C) $( - \infty , - 5 ) \cup ( - 5,7 ) \cup ( 7 , \infty )$
D) $( - \infty , \infty )$

Accepted Answer

The function $r(x) = x^2 + 2x - 35$ is a polynomial, and polynomials are defined for all real numbers, hence the domain is all real numbers.

Question 11

Solve the problem.
-A student decides to finance a used car over a 5-yr (60-month) period. After making a down payment of $\$ 5,000$, the remaining cost of the car including tax and interest is $\$ 13,140$. The amount owed $y = A ( t )$ (in \$) is given by $A ( t ) = 13,140 - 219 t$, where $t$ is the number of months after purchase and $0 \leq t \leq 60$. Determine the $t$-intercept and $y$-intercept.
Amount Owed on Vehicles after $t$ Months

A) $t$-intercept: $( 0,60 ) ; y$-intercept: $( 13,140,0 )$
B) $t$-intercept: $( 60,0 ) ; y$-intercept: $( 0,13,140 )$
C) $t$-intercept: $( 13,140,0 ) ; y$-intercept: $( 0,60 )$
D) $t$-intercept: $( 0,13,140 ) ; y$-intercept: $( 60,0 )$

Accepted Answer

The answer of Solve the problem.
-A student decides to finance...

Question 12

Write the domain in interval notation.
-$$r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }$$
A) $( \infty , 0 ) \cup ( 0 , \infty )$
B) $( \infty , \infty )$
C) $( \infty , - 9 ) \cup ( 9 , \infty )$
D) $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$

Accepted Answer

The denominator $x^2 + 81$ is never zero for any real value of $x$, because $x^2$ is always non-negative, and adding 81 ensures the expression is always positive. Therefore, the function is defined for all real numbers, which is represented by $(-\infty, \infty)$.

Question 13

Use the graph of y = f (x) to answer the questions.
-a. Determine $f ( - 1 )$
b. Find the range of $f$.

A) $f ( - 1 ) = 1$; Range: $[ - 2 , \infty )$
B) $f ( - 1 ) = - 2 ;$ Range: $[ - 2 , \infty )$
C) $f ( - 1 ) = 1 ;$ Range: $\{ - 2 \} \cup [ 0 , \infty )$
D) $f ( - 1 ) = - 2 ;$ Range: $\{ - 2 \} \cup [ 0 , \infty )$

Accepted Answer

The answer of Use the graph of y = f...

Question 14

Write the domain in interval notation.
-$$a ( x ) = \sqrt { 8 - x }$$
A) $( - \infty , 8 ]$
B) $( - 8 , \infty )$
C) $[ - 8 , \infty )$
D) $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Accepted Answer

For the square root function to be defined, the expression inside the square root, $8 - x$, must be greater than or equal to 0. Solving $8 - x \geq 0$ gives $x \leq 8$, which corresponds to the interval $(-\infty, 8]$.

Question 15

Write the domain in interval notation.
-$$y ( t ) = \sqrt { 8 - t }$$
A) $( - \infty , 8 )$
B) $( - \infty , 8 ]$
C) $( - \infty , \infty )$
D) $[ 0,16 ]$

Accepted Answer

The domain of the function $y(t) = \sqrt{8 - t}$ consists of all values of $t$ for which the expression under the square root, $8 - t$, is greater than or equal to 0. Solving the inequality $8 - t \geq 0$ gives $t \leq 8$. Therefore, the domain in interval notation is $(- \infty, 8]$, which includes 8 because the square root of 0 is defined.

Question 16

Use the graph of y = f (x) to answer the questions.
-a. Determine $f ( - 1 )$
b. Find all $x$ for which $f ( x ) = - 4$

A) $f ( - 1 ) = - 4 ; f ( x ) = - 4$ for $x = 4$
B) $f ( - 1 ) = 1 ; f ( x ) = - 4$ for all $x$ on the interval $( - 1,2 )$
C) $f ( - 1 ) = 1 ; f ( x ) = - 4$ for $x = 4$
D) $f ( - 1 ) = - 4 ; f ( x ) = - 4$ for all $x$ on the interval $( - 1,2 )$

Accepted Answer

The answer of Use the graph of y = f...

Question 17

Write the domain in interval notation.
-$$z ( a ) = \sqrt { a + 9 }$$
A) $[ 0 , \infty )$
B) $( - \infty , \infty )$
C) $[ - 9 , \infty )$
D) $( - 9 , \infty )$

Accepted Answer

The domain of the function $z(a) = \sqrt{a + 9}$ consists of all values of $a$ for which the expression under the square root, $a + 9$, is greater than or equal to 0. Solving $a + 9 \geq 0$ gives $a \geq -9$, which is represented by the interval $[-9, \infty)$.

Question 18

Determine the domain and range of the function.
-
A) Domain: $( - \infty , - 1 ]$; Range: $[ - 2 , \infty )$
B) Domain: $[ - 2 , \infty )$; Range: $( - \infty , - 1 ]$
C) Domain: $( - 2 , \infty )$; Range: $( - \infty , - 1 )$
D) Domain: $[ - 2 , \infty ] )$; Range $[ - 3 , - \infty )$

Accepted Answer

The answer of Determine the domain and range of the...

Question 19

Write the domain in interval notation.
-$$g ( t ) = \sqrt [ 3 ] { 5 - t }$$
A) $( - \infty , 5 ]$
B) $[ 5 , \infty )$
C) $( - \infty , 5 ) \cup ( 5 , \infty )$
D) $( - \infty , \infty )$

Accepted Answer

The cube root function, $\sqrt[3]{x}$, is defined for all real numbers, meaning there are no restrictions on the values that $5 - t$ can take. Therefore, the domain of $g(t) = \sqrt[3]{5 - t}$ is all real numbers, which is represented by $( - \infty , \infty )$.

Question 20

Write the domain in interval notation.
-$$f ( x ) = \frac { x - 4 } { x - 5 }$$
A) $( - \infty , \infty )$
B) $( - \infty , 5 ) \cup ( 5 , \infty )$
C) $( ( - \infty , - \sqrt { 5 } ) \cup ( - \sqrt { 5 } , \sqrt { 5 } ) \cup ( \sqrt { 5 } , \infty )$
D) $( - \infty , 4 ) \cup ( 4 , \infty )$

Accepted Answer

The function is undefined at $x = 5$ because it would result in division by zero. Everywhere else, the function is defined. Hence, the domain excludes only $x = 5$, which is represented by the interval notation $( - \infty , 5 ) \cup ( 5 , \infty )$.

Quiz 2: Functions and Relations

Write the domain in interval notation. - $f ( x ) = \frac { 4 } { \sqrt { 3 - x } }$

Write the domain in interval notation. - $h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$

Write the domain in interval notation. - $w ( a ) = \frac { 4 } { 6 - | a - 3 | }$

Write the domain in interval notation. - $p ( x ) = 7 x + 1 ; x \geq 0$

Write the domain in interval notation. - $f ( x ) = \frac { x + 7 } { x + 3 }$

Write the domain in interval notation. - $k ( x ) = \frac { x + 9 } { x - 4 }$

Write the domain in interval notation. - $m ( x ) = \frac { 5 } { | x | + 1 }$

Write the domain in interval notation. - $r ( x ) = x ^ { 2 } + 2 x - 35$

Write the domain in interval notation. - $r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }$

Write the domain in interval notation. - $a ( x ) = \sqrt { 8 - x }$

Write the domain in interval notation. - $y ( t ) = \sqrt { 8 - t }$

Use the graph of y = f (x) to answer the questions. -a. Determine $f ( - 1 )$ b. Find all $x$ for which $f ( x ) = - 4$

Write the domain in interval notation. - $z ( a ) = \sqrt { a + 9 }$

Write the domain in interval notation. - $g ( t ) = \sqrt [ 3 ] { 5 - t }$

Write the domain in interval notation. - $f ( x ) = \frac { x - 4 } { x - 5 }$

Quiz 2: Functions and Relations

Write the domain in interval notation. - f(x) =43−xf ( x ) = \frac { 4 } { \sqrt { 3 - x } }f(x) =3−x​4​

Write the domain in interval notation. - h(c) =2c+11−1h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }h(c) =c+11​−12​

Write the domain in interval notation. - w(a) =46−∣a−3∣w ( a ) = \frac { 4 } { 6 - | a - 3 | }w(a) =6−∣a−3∣4​

Determine the domain and range of the function. -

Write the domain in interval notation. - p(x) =7x+1;x≥0p ( x ) = 7 x + 1 ; x \geq 0p(x) =7x+1;x≥0

Determine the domain and range of the function. -

Write the domain in interval notation. - f(x) =x+7x+3f ( x ) = \frac { x + 7 } { x + 3 }f(x) =x+3x+7​

Write the domain in interval notation. - k(x) =x+9x−4k ( x ) = \frac { x + 9 } { x - 4 }k(x) =x−4x+9​

Write the domain in interval notation. - m(x) =5∣x∣+1m ( x ) = \frac { 5 } { | x | + 1 }m(x) =∣x∣+15​

Write the domain in interval notation. - r(x) =x2+2x−35r ( x ) = x ^ { 2 } + 2 x - 35r(x) =x2+2x−35

Write the domain in interval notation. - r(x) =−14x2+81r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }r(x) =x2+81−14​

Use the graph of y = f (x) to answer the questions. -a. Determine f(−1) f ( - 1 ) f(−1) b. Find the range of fff .

Write the domain in interval notation. - a(x) =8−xa ( x ) = \sqrt { 8 - x }a(x) =8−x​

Write the domain in interval notation. - y(t) =8−ty ( t ) = \sqrt { 8 - t }y(t) =8−t​

Use the graph of y = f (x) to answer the questions. -a. Determine f(−1) f ( - 1 ) f(−1) b. Find all xxx for which f(x) =−4f ( x ) = - 4f(x) =−4

Write the domain in interval notation. - z(a) =a+9z ( a ) = \sqrt { a + 9 }z(a) =a+9​

Determine the domain and range of the function. -

Write the domain in interval notation. - g(t) =5−t3g ( t ) = \sqrt [ 3 ] { 5 - t }g(t) =35−t​

Write the domain in interval notation. - f(x) =x−4x−5f ( x ) = \frac { x - 4 } { x - 5 }f(x) =x−5x−4​

Write the domain in interval notation. - $f ( x ) = \frac { 4 } { \sqrt { 3 - x } }$

Write the domain in interval notation. - $h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$

Write the domain in interval notation. - $w ( a ) = \frac { 4 } { 6 - | a - 3 | }$

Write the domain in interval notation. - $p ( x ) = 7 x + 1 ; x \geq 0$

Write the domain in interval notation. - $f ( x ) = \frac { x + 7 } { x + 3 }$

Write the domain in interval notation. - $k ( x ) = \frac { x + 9 } { x - 4 }$

Write the domain in interval notation. - $m ( x ) = \frac { 5 } { | x | + 1 }$

Write the domain in interval notation. - $r ( x ) = x ^ { 2 } + 2 x - 35$

Write the domain in interval notation. - $r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }$

Write the domain in interval notation. - $a ( x ) = \sqrt { 8 - x }$

Write the domain in interval notation. - $y ( t ) = \sqrt { 8 - t }$

Use the graph of y = f (x) to answer the questions. -a. Determine $f ( - 1 )$ b. Find all $x$ for which $f ( x ) = - 4$

Write the domain in interval notation. - $z ( a ) = \sqrt { a + 9 }$

Write the domain in interval notation. - $g ( t ) = \sqrt [ 3 ] { 5 - t }$

Write the domain in interval notation. - $f ( x ) = \frac { x - 4 } { x - 5 }$