Deck 6: A Library of Parent Functions

Question 1

Select the correct graph of the given function.? $$f ( x ) = 2.7 x - 5.5$$ ?

A)?
B)?
C)?
D)?
E)?

Answer 1

?

Question 2

Select the correct graph of the given function.? $$f ( x ) = 1 + \frac { 1 } { x }$$ ?

A)?
B)?
C)?
D)?
E)?

Answer 2

?

Question 3

Select the correct graph of the given function.? $$f ( x ) = x ^ { 6 } - 6$$ ?

A)?
B)?
C)?
D)?
E)?

Answer 3

?

Question 4

Select the correct graph of the given function.? $$f ( x ) = ( x - 3 ) ^ { 3 } - 3$$ ?

A)?
B)?
C)?
D)?
E)?

Question 5

Identify the following function.? $f ( x ) = 8$ ?

A)Constant function
B)Absolute value function
C)Square root function
D)Squaring function
E)Identity function

Question 6

Select the linear function such that it has the indicated function values.? $f ( 8 ) = 16 , f ( - 3 ) = - 17$ ?

A) $f ( x ) = 3 x - 8$
B) $f ( x ) = - 3 x + 3$
C) $f ( x ) = 3 x + 8$
D) $f ( x ) = 8 x + 3$
E) $f ( x ) = - 3 x - 3$

Question 7

Select the correct graph of the given function.? $$f ( x ) = - 3 x ^ { 3 }$$ ?

A)?
B)?
C)
D)?
E)?

Question 8

Select the correct graph of the given function.? $f ( x ) = - x + 5$ ?

A)?
B)?
C)?
D)?
E)?

Question 9

Select the correct graph of the given function.? $$f ( x ) = 1 - 2 \sqrt { x }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 10

Select the correct graph of the given function.? $$f ( x ) = - \frac { 8 } { x }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 11

Select the correct graph of the given function.? $$f ( x ) = \sqrt { x + 1 } + 2$$ ?

A)?
B)?
C)?
D)?
E)?

Question 12

Select the correct graph for the given function.? $$f ( x ) = 6 ( x + 3 ) ^ { 3 } - 1$$ ?

A)?
B)?
C)?
D)?
E)?

Question 13

Select the correct graph of the given function.? $$f ( x ) = 5 x ^ { 2 } - 1$$ ?

A)?
B)?
C)?
D)?
E)?

Question 14

Select the correct graph of the given function.? $$f ( x ) = \frac { 1 } { x + 1 }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 15

Select the correct graph of the given function.? $$f ( x ) = - \frac { 1 } { 6 } x - \frac { 5 } { 2 }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 16

Select the linear function such that it has the indicated function values.? $f ( - 4 ) = - 2 , f ( 4 ) = - 2$ ? ?

A)f(x)= -x
B)f(x)= 2
C)f(x)= -2
D)f(x)= 4
E)f(x)= x

Question 17

Select the correct graph of the given function.? $$f ( x ) = 2 - x ^ { 2 }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 18

Select the correct graph of the given function.? $$f ( x ) = 1.5 - 2 x ^ { 2 }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 19

Select the linear function such that it has the indicated function values.? $f ( 1 ) = 8 , f ( 0 ) = 7$ ?

A) $f ( x ) = 4 x + 7$
B) $f ( x ) = x + 7$
C) $f ( x ) = 7 x - 3$
D) $f ( x ) = x - 7$
E) $f ( x ) = - 7 x - 7$

Question 20

Select the correct graph for the given function.? $$f ( x ) = 2 \sqrt { x }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 21

Select the correct graph of the given function.? $$f ( x ) = | x + 3 |$$ ?

A)?
B)?
C)?
D)?
E)?

Question 22

Evaluate the function h(x)= [[x + 9]] for x = -4. ​

A)​h(x)= 13
B)​h(x)= 5
C)​h(x)= 9
D)​h(x)= -13
E)​h(x)= -5

Question 23

Select the graph of the function: f(x)= [[x + 3]]. ​
​

A)​
B)​
C)​
D)​
E)​

Question 24

Select the graph of the function.? $$f ( x ) = \left\{ \begin{array} { c c } 5 - x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 0 \\x ^ { 2 } + 3 & x \geq 0\end{array} \right.$$ ?

A)?
B)?
C)?
D)?
E)?

Question 25

Select the correct graph of the given function.? $$f ( x ) = \frac { 1 } { x - 4 }$$ ?

A)?
B)?
C)?
D)?
E)?

Question 26

Evaluate the function f(x)= [[3x + 1]] for x = 4. ​

A)f(x)= -4
B)​ f(x)= 4
C)​ f(x)= 11
D)​ f(x)= 13
E)​ f(x)= 12

Question 27

Select the correct graph of the given function.? $$f ( x ) = 2 - | x |$$ ?

A)?
B)?
C)?
D)?
E)?

Question 28

Select the graph of the function.? $$f ( x ) = \left\{ \begin{array} { l l } 3 - x ^ { 2 } & x < 0 \\x ^ { 2 } + 2 & x \geq 0\end{array} \right.$$ ?

A)?
B)?
C)?
D)?
E)?

Question 29

Select the graph of the function: f(x)= [[x]] - 4. ​
​

A)​
B)​
C)​
D)​
E)​

Question 30

Select the correct graph of the given function.? $$f ( x ) = | x | - 2$$ ?

A)?
B)?
C)?
D)?
E)?

Question 31

Select the graph of the function f(x)= [[x - 4]]. ​

A)​
B)​
C)​
D)​
E)​

Question 32

Evaluate the function f(x)= 3[[3x - 1]] + 5 for x = 6. ​

A)​f(x)= 51
B)​f(x)= -6
C)​f(x)= 56
D)​f(x)= 6
E)​f(x)= 46

Question 33

Select the graph of the function. $$f ( x ) = \left\{ \begin{array} { l l } 2 x + 1 & x < 0 \\1 - x & x \geq 0\end{array} \right.$$

A)?
B)?
C)?
D)?
E)?

Question 34

Select the graph of the function.? $$f ( x ) = \left\{ \begin{array} { c c } 3 + x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 2 \\x ^ { 2 } + 7 & x \geq 2\end{array} \right.$$ ?

A)?
B)?
C)?
D)?
E)?

Question 35

Select the correct graph of the given function.? $$f ( x ) = | x - 6 |$$ ?

A)?
B)?
C)?
D)?
E)?

Question 36

Evaluate the function h(x)= 2[[x]] for x = -4. ​

A)​h(x)= -8
B)​h(x)= -6
C)​​h(x)= 4
D)​h(x)= -4
E)​h(x)= -2

Question 37

Select the graph of the function f(x)= 3[[x]]. ​

A)
B)​
C)​
D)​
E)​

Question 38

Evaluate the function $$h ( x ) = \left[ \left[ \frac { 1 } { 2 } x + 9 \right] \right]$$ for x = 6. ?

A)?h(x)= 9
B)?h(x)= 3
C)?h(x)= -12
D)?h(x)= 12
E)?h(x)= -3

Question 39

Evaluate the function f(x)= 2[[x]] + 7 for x = -7. ​

A)​ f(x)= -21
B)​ f(x)= 2
C)​ f(x)= -2
D)​ f(x)= -7
E)​ f(x)= 7

Question 40

Evaluate the function f(x)= [[x]] for x = 9.2. ​

A)​f(x)= 2
B)​f(x)= 10
C)​f(x)= 9
D)​f(x)= -9
E)​f(x)= 11

Question 41

The cost of sending an overnight package from Los Angeles to Miami is $26.30 for a package weighing up to but not including 1 pound and $4.00 for each additional pound or portion of a pound.A model for the total cost C (in dollars)of sending the package is ​
С = 26.30 + 4.00[[x]],x > 0,where x is the weight in pounds.
​
Select the graph of the model.
​

A)​
B)​
C)​
D)​
E)​

Question 42

?Write the linear function f such that it has the indicated values. ?f (-1)= -5,f (-9)= -6
?

A)?y = $- \frac { 3 } { 4 }$ x+ $\frac { 17 } { 3 }$
B)?y = 8 x+ 3
C)?y = $\frac { 1 } { 8 }$ x $- \frac { 41 } { 8 }$
D)?y = $\frac { 1 } { 8 }$ x $- \frac { 39 } { 8 }$
E)?y = $- \frac { 4 } { 3 }$ x $- \frac { 11 } { 3 }$

Question 43

Evaluate the function for the indicated values. f (x)= 5[[x + 3]] - 5
(i)f (3)
(ii)f (-63.30)
(iii)f ( $\frac { 7 } { 8 }$ )
?

A)(i)25 (ii)-305 (iii)15
B)?(i)25 (ii)-305 (iii)10
C)?(i)26 (ii)-310 (iii)15
D)?(i)26 (ii)-310 (iii)10
E)?(i)25 (ii)-310 (iii)10

Question 44

The cost of sending an overnight package from Los Angeles to Miami is $26.40 for a package weighing up to but not including 1 pound and $3.25 for each additional pound or portion of a pound.A model for the total cost C (in dollars)of sending the package is ​
С = 26.40 + 3.25[[x]] ,x > 0,where x is the weight in pounds.
​
Determine the cost of sending a package that weighs 5.25 pounds.
​

A)$45.65
B)​$44.65
C)​$43.65
D)​$46.65
E)​$42.65

Question 45

Which graph represents the function?? $$g ( x ) = 2 [ [ x ] ]$$ ?

A)
B)
C)
D)
E)

Question 46

Which function does the graph represent?

A)​g(x)= [[3x]]
B)​g(x)= [[x+3]]
C)​g(x)= 3[[x]]
D)​g(x)= [[-4x]]
E)​g(x)= [[x-3]]

Question 47

A mechanic is paid $13.00 per hour for regular time and time-and-a-half for overtime.The weekly wage function is given by? $$W ( h ) = \left\{ \begin{array} { l l } 13 h & 0 < h \leq 40 \\21 ( h - 40 ) + 520 & h > 40\end{array} \right.$$ ? where h is the number of hours worked in a week.
?
Evaluate W(30),W(50).
?

A)?W(30)= 410,W(50)= 750
B)?W(30)= 430,W(50)= 770
C)?W(30)= 400,W(50)= 740
D)?W(30)= 390,W(50)= 730
E)?W(30)= 420,W(50)= 760

Question 48

Which graph represents the function?? $$f ( x ) = \left\{ \begin{array} { l } - 3 x , x < 0 \\x - 3 , x \geq 0\end{array} \right.$$ ?

A)?
B)?
C)?
D)?
E)?

Question 49

The cost of sending an overnight package from Los Angeles to Miami is $25.00 for a package weighing up to but not including 1 pound and $3.50 for each additional pound or portion of a pound.Use the greatest integer function to create a model for the cost C of overnight delivery of a package weighing x pounds,x > 0. ​

A)​C = 25.00 - 3.50[[x]],x > 0
B)​C = 25.00 + 3.50[[x]],x > 0
C)​C = -25.00 + 3.50[[x]],x > 0
D)​С = -25.00 - 3.50 [[x]],x > 0
E)​C = 25.00[[x]] + 3.50,x > 0

Question 50

The table shows the monthly revenue y (in thousands of dollars)of a landscaping business for each month of the year 2008,with x = 1 representing January.
$$\begin{array} { | c | c | } \hline x & y \\\hline 1 & 6.0 \\\hline 2 & 6.1 \\\hline 3 & 7.1 \\\hline 4 & 9.2 \\\hline 5 & 12.3 \\\hline 6 & 16.4 \\\hline 7 & 12.2 \\\hline 8 & 10.2 \\\hline 9 & 8.3 \\\hline 10 & 6.3 \\\hline 11 & 4.3 \\\hline 12 & 2.4 \\\hline\end{array}$$
A mathematical model that represents these data is: $$f ( x ) = \left\{ \begin{array} { l l } 0.505 x ^ { 2 } - 1.47 x + 7.0 & 1 \leq x \leq 6 \\- 1.97 x + 26.0 & 6 < x \leq 12\end{array} \right.$$
Find f (1)and f (12).

A) $f ( 1 ) = 2.860 , f ( 12 ) = 6.79$
B) $f ( 1 ) = 3.360 , f ( 12 ) = 7.04$
C) $f ( 1 ) = 6.035 , f ( 12 ) = 2.36$
D) $f ( 1 ) = 2.860 , f ( 12 ) = 6.54$
E) $f ( 1 ) = 2.860 , f ( 12 ) = 6.29$