Question 1

Give a rule for the piecewise-defined function. Then give the domain and range.
-$f(x)=2[x]$

A)

B)

C)

D)

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 2

Give a rule for the piecewise-defined function. Then give the domain and range.
-
A) $f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \ x + 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 1 ) \cup [ 5 , \infty )$
B) $f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \ x - 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , 1 ) \cup [ 5 , \infty )$, Range: $( \infty , \infty )$
C) $f ( x ) = \left\{ \begin{array} { l l } \sqrt [ 3 ] { x } & \text { if } x < 1 ; \text { Domain: } ( \infty , \infty ) , \text { Range: } ( \infty , 1 ) \cup [ 5 , \infty ) \ x + 4 & \text { if } x \geq 1 \end{array} \right.$
D) $f ( x ) = \left\{ \begin{array} { l l } - x ^ { 3 } & \text { if } x < 1 \ x - 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , 1 ) \cup [ 5 , \infty )$, Range: $( \infty , \infty )$

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 3

The charges for renting a moving van are $\$ 65$ for the first 40 miles and $\$ 5$ for each additional mile. Assume that a fraction of a mile is rounded up. (i) Determine the cost of driving the van 84 miles. (ii) Find a symbolic representation for a function $\mathrm { f }$ that computes the cost of driving the van $x$ miles, where $0 < x \leq 100$. (Hint: express $\mathrm { f }$ as a piecewise-constant function.)
A) $\$ 685 ; f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 5 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$
B) $\$ 685 ; f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 5 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$
C) $\$ 285 ; f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 5 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$
D) $\$ 5680 ; f ( x ) = \left\{ \begin{array} { l l } 65 x & \text { if } 0 < x \leq 40 \ 65 + 5 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$

Accepted Answer

For the first part, driving the van 84 miles costs $ \$ 65 $ for the first 40 miles plus $ \$ 5 $ for each of the additional 44 miles, which is $ \$ 65 + 44 \times \$ 5 = \$ 65 + \$ 220 = \$ 285 $. For the second part, the cost function $ f(x) $ is $ \$ 65 $ for the first 40 miles and then $ \$ 65 + \$ 5 $ for each mile over 40, correctly represented as $ 65 + 5(x - 40) $ for $ 40 < x \leq 100 $.

Question 4

Give a rule for the piecewise-defined function. Then give the domain and range.
-$\mathrm{f}(\mathrm{x})=\llbracket \mathrm{x} \rrbracket \rrbracket+1$

A)

B)

C)

D)

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 5

Suppose a car rental company charges $72 for the first day and $22 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(5.5).
A) $193
B) $121
C) $171
D) $182

Accepted Answer

The cost for the first day is $72, and for the remaining 4.5 days, the cost is $22 per day. So, S(5.5) = $72 + (4.5 * $22) = $72 + $99 = $171. However, since any partial day is charged as a full day, it should be 5 additional days: S(5.5) = $72 + (5 * $22) = $72 + $110 = $182.

Question 6

Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?
A) $65
B) $30
C) $50
D) $70

Accepted Answer

The cost for 10 units of coverage is calculated as $20 for the first unit plus $5 for each of the remaining 9 units. So, $20 + (9 * $5) = $20 + $45 = $65.

Question 7

Describe how the graph of the equation relates to the graph $$y = x ^ { 2 }$$
-$f ( x ) = ( x - 2 ) ^ { 2 }$
A) a translation 2 units to the left
B) a translation 2 units up
C) a translation 2 units down
D) a translation 2 units to the right

Accepted Answer

The graph of $f(x) = (x - 2)^2$ is a translation of the graph $y = x^2$ 2 units to the right, as the subtraction inside the parentheses shifts the graph in the opposite direction of the sign.

Question 8

Give a rule for the piecewise-defined function. Then give the domain and range.
-$f(x)=\llbracket x+1]$

A)

B)

C)

D)

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 9

Give a rule for the piecewise-defined function. Then give the domain and range.
-
A) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x \leq 0 \ - x & \text { if } x > 0 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 0 ) \cup \{ 5 \}$
B) $f ( x ) = \left\{ \begin{array} { l } 5 \text { if } x < 0 \ x \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , 0 ] \cup ( 5 )$, Range: $( \infty , \infty )$
C) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - 5 x & \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , 0 ) \cup \{ 5 \}$, Range: $( \infty , \infty )$
D) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - x & \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 0 ] \cup \{ 5 \}$

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 10

Sketch a graph showing the distance (in miles) that a person is from home after x hours if that individual drives at 30 mph to a lake 60 miles away, stays at the lake 1.5 hours, and then returns home at a speed of 60 mph.  
A) 
B) none of these
C) 
D)

Accepted Answer

The answer of Sketch a graph showing the distance (in...

Question 11

Give a rule for the piecewise-defined function. Then give the domain and range.
-
A) $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \ x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , \infty )$
B) $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \leq 1 \ x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , \infty )$
C) $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \ x + 2 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( \infty , 2 ) \cup ( 2 , \infty )$, Range: $( \infty , \infty )$
D) $f ( x ) = \left\{ \begin{array} { l l } - x & \text { if } x \leq 1 \ 2 x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 2 ) \cup ( 2 , \infty )$

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 12

Give a rule for the piecewise-defined function. Then give the domain and range.
-$f(x)=\llbracket x \rrbracket-1$

A)

B)

C)

D)

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 13

The table lists the average composite scores on a national entrance exam for selected years. $$\begin{array} { c | c c c c c c c } 
\text { Year } & 2 & 4 & 6 & 8 & 10 & 12 & 14 \
\hline \text { Score } & 122.7 & 131.5 & 131.5 & 129.5 & 133.9 & 132.0 & 130.0
\end{array}$$ (i) Make a line graph of the data. (ii) If the graph represents a piecewise-linear function f, find a symbolic representation for the piece of f located on
The interval [4, 6]. 
A) $$f ( x ) = 4.4 x - 8589.3 \text { if } 8 \leq x \leq 10$$

B) $$f ( x ) = 131.5 \text { if } 4 \leq x \leq 6$$

C) none of these
D) $$f ( x ) = 0.75 x - 1355 \text { if } 4 \leq x \leq 8$$

Accepted Answer

The answer of The table lists the average composite scores...

Question 14

A video rental company charges $5 per day for renting a video tape, and then $4 per day after the first. Use the greatest integer function and write an expression for renting a video tape for x days.
A) $y = 4 x + 5$
B) $y + 5 = 4 \llbracket x \rrbracket$
C) $y = \llbracket 4 x + 5 \rrbracket$
D) $y = 4 \llbracket x - 1 \rrbracket + 5$

Accepted Answer

The correct expression accounts for the $5 charge on the first day and then $4 for each additional day. The greatest integer function is applied to $x-1$ to calculate the number of days after the first, ensuring the first day is charged at $5, and subsequent days at $4.

Question 15

Describe how the graph of the equation relates to the graph $$y = x ^ { 2 }$$
-$f ( x ) = x ^ { 2 } + 7$
A) a translation 7 units to the right
B) a translation 7 units up
C) a translation 7 units to the left
D) a translation 7 units down

Accepted Answer

The graph of $f(x) = x^2 + 7$ is a vertical translation of the graph $y = x^2$ upwards by 7 units.

Question 16

In Country X, the average hourly wage in dollars from 1960 to 2010 can be modeled by $$f ( x ) = \left\{ \begin{array} { l l } 
0.077 ( x - 1960 ) + 0.39 & \text { if } 1960 \leq x < 1995 \
0.189 ( x - 1995 ) + 3.06 & \text { if } 1995 \leq x \leq 2010
\end{array} \right.$$ Use f to estimate the average hourly wages in 1965, 1985, and 2005.
A) $3.45, $0.39, $6.84
B) $0.78, $2.32, $6.84
C) $0.78, $3.06, $6.84

Accepted Answer

The average hourly wage in 1965 is f(1965) = 0.077(1965 - 1960) + 0.39 = $0.78.The average hourly wage in 1985 is f(1985) = 0.077(1985 - 1960) + 0.39 = $2.32.The average hourly wage in 2005 is f(2005) = 0.189(2005 - 1995) + 3.06 = $6.84.

Question 17

Give a rule for the piecewise-defined function. Then give the domain and range.
-
A) $f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 3 ] \cup [ 3 , \infty )$
B) $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 3 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , 3 ] \cup [ 3 , \infty )$, Range: $( \infty , \infty )$
C) $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 3 ) \cup ( 3 , \infty )$
D) $f ( x ) = \left\{ \begin{array} { l } 2 x - 3 \text { if } x < 3 \ 2 x + 3 \text { if } x \geq 3 \end{array} ; \right.$ Domain: $( \infty , 3 ) \cup ( 3 , \infty )$, Range: $( \infty , \infty )$

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Question 18

Employees of a publishing company received an increase in salary of 3% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(15,000).
A) $13,883
B) $20,200
C) $16,150
D) $15,700

Accepted Answer

The new salary S(x) is calculated as the previous salary x increased by 3% plus a $700 bonus. For x = $15,000, S(15,000) = 15,000 * 1.03 + 700 = 16,150.

Question 19

Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let $L ( x )$ be the cost of mailing a letter weighing $x$ ounces. Graph $y = L ( x )$.

A)

B)

C)

D)

Accepted Answer

The answer of Assume it costs 25 cents to mail...

Question 20

Give a rule for the piecewise-defined function. Then give the domain and range.
-$f(x)=\llbracket x-1 \rrbracket$

A)

B)

C)

D)

Accepted Answer

The answer of Give a rule for the piecewise-defined function....

Quiz 3: Graphs and Functions

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =2[x]$

Suppose a car rental company charges $72 for the first day and $22 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(5.5) .

Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = ( x - 2 ) ^ { 2 }$

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =\llbracket x+1]$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =\llbracket x+1] A) B) C) D)$

Sketch a graph showing the distance (in miles) that a person is from home after x hours if that individual drives at 30 mph to a lake 60 miles away, stays at the lake 1.5 hours, and then returns home at a speed of 60 mph.

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =\llbracket x \rrbracket-1$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =\llbracket x \rrbracket-1 A) B) C) D)$

A video rental company charges $5 per day for renting a video tape, and then $4 per day after the first. Use the greatest integer function and write an expression for renting a video tape for x days.

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = x ^ { 2 } + 7$

Employees of a publishing company received an increase in salary of 3% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(15,000) .

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =\llbracket x-1 \rrbracket$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =\llbracket x-1 \rrbracket A) B) C) D)$

Quiz 3: Graphs and Functions

Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =2[x]f(x) =2[x]f(x) =2[x]

Give a rule for the piecewise-defined function. Then give the domain and range. -

Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =⟦x⟧⟧+1\mathrm{f}(\mathrm{x}) =\llbracket \mathrm{x} \rrbracket \rrbracket+1f(x) =[[x]]]]+1

Suppose a car rental company charges $72 for the first day and $22 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(5.5) .

Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?

Describe how the graph of the equation relates to the graph y=x2y = x ^ { 2 }y=x2 - f(x) =(x−2) 2f ( x ) = ( x - 2 ) ^ { 2 }f(x) =(x−2) 2

Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =⟦x+1]f(x) =\llbracket x+1]f(x) =[[x+1]

Give a rule for the piecewise-defined function. Then give the domain and range. -

Sketch a graph showing the distance (in miles) that a person is from home after x hours if that individual drives at 30 mph to a lake 60 miles away, stays at the lake 1.5 hours, and then returns home at a speed of 60 mph.

Give a rule for the piecewise-defined function. Then give the domain and range. -

Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =⟦x⟧−1f(x) =\llbracket x \rrbracket-1f(x) =[[x]]−1

A video rental company charges $5 per day for renting a video tape, and then $4 per day after the first. Use the greatest integer function and write an expression for renting a video tape for x days.

Describe how the graph of the equation relates to the graph y=x2y = x ^ { 2 }y=x2 - f(x) =x2+7f ( x ) = x ^ { 2 } + 7f(x) =x2+7

Give a rule for the piecewise-defined function. Then give the domain and range. -

Employees of a publishing company received an increase in salary of 3% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(15,000) .

Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) L ( x ) L(x) be the cost of mailing a letter weighing xxx ounces. Graph y=L(x) y = L ( x ) y=L(x) .

Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =⟦x−1⟧f(x) =\llbracket x-1 \rrbracketf(x) =[[x−1]]

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =2[x]$

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = ( x - 2 ) ^ { 2 }$

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =\llbracket x+1]$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =\llbracket x+1] A) B) C) D)$

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =\llbracket x \rrbracket-1$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =\llbracket x \rrbracket-1 A) B) C) D)$

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = x ^ { 2 } + 7$

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x) =\llbracket x-1 \rrbracket$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x) =\llbracket x-1 \rrbracket A) B) C) D)$