# Worksheet: Evaluating Functions

In this worksheet, we will practice calculating the value (or output) of a function using its equation or its graph.

Q1:

Which of the following set of coordinates lies on ?

• A
• B
• C
• D

Q2:

Find , given the point lies on the function .

Q3:

Several fish were accidentally released into a lake. After weeks, the number of fish is estimated to be . Determine the likely number of fish in the lake after 5 weeks. Give your answer to the nearest whole number.

Q4:

Find given the function .

Q5:

Given that the function , where , determine .

Q6:

Using the function , calculate the corresponding output for an input of 2.

Q7:

Find the value of given the function and the function .

Q8:

Complete the given table of values for the function .

 𝑥 𝑦 −2 −1 0 1 2
• A
• B
• C
• D
• E

Q9:

Complete the given table of values for the function .

 𝑥 𝑦 −2 −1 0 1 2
• A
• B
• C
• D
• E

Q10:

Given that the point lies on the graph of , find .

• A
• B
• C
• D
• E

Q11:

If , find .

• A
• B
• C
• D
• E266

Q12:

Find , given the point lies on the function .

Q13:

Which of the following set of coordinates lies on ?

• A
• B
• C
• D

Q14:

Which of the following is NOT a point on the curve ?

• A
• B
• C
• D
• E

Q15:

A function maps the positive integers onto a set . For example, if then would be the set of even integers

What sequence is produced by inputing the positive integers into .

• A
• B
• C
• D
• E

Which of the following describes ?.

• A19 is the ninth positive odd integer.
• B19 is the tenth positive odd integer.
• C19 is the eleventh positive odd integer.
• D19 is the eighth positive odd integer.
• E19 is the sixth positive odd integer.

Write the first 5 terms of the sequence given by .

• A
• B
• C
• D
• E

Which of the following functions produces the sequence ?

• A
• B
• C
• D
• E

Q16:

Given a function , the meaning of is “the output when the input is 1 less than .” Interpret the following.

• A3 more than the output when the input is
• Bthe output when the input is 3 more than
• C times the output
• D times the input
• Ethe input when the ouput is 3 more than

• A3 less than the output when the input is
• B3 more than the input when the output is
• C3 less than the input when the output is
• DThe output is 3 when the input is .
• E3 more than the output when the input is

• Athe output when the input is less than 3
• Bthe output when the input is more than 3
• Cthe input when the ouput is less than 3
• Dthe input when the ouput is more than 3

• Athe change in input when the output changes from to
• Bthe change in output when the input changes from to
• Cthe change in output when the input changes from to
• Dthe change in input when the output changes from to

• Athe output when the input is
• B3 more than the output when the input is
• Cthe output when the input is 3 times
• Dthe input when the output is 3 times
• Ethe output when the input is 3

• Athe result of raising the input at output to the th power
• Bthe result of raising the output at input to the th power
• Cthe result of raising the input at output to the th power
• Dthe result of raising the output at input to the th power

Q17:

The function records Benjamin’s distance in kilometers from his home minutes after he begins the measurements. Write the given statements in words.

• ABenjamin reaches his home after 0.5 km.
• BBenjamin starts measurement when he is more than 0.5 km from home.
• CBenjamin starts measurements when he is 0.5 km from home.
• DBenjamin starts measurements when he is at home.

• ABenjamin starts measurements when he is 60 minutes from home.
• BBenjamin starts measurements when he is 60 km from home.
• CBenjamin is home after an hour.

• ABenjamin is at different distances from home at both the 23rd and 32nd minute.
• BBenjamin is the same time from home at both the 23rd and 32nd kilometer.
• CBenjamin is the same distance from home at both the 23rd and 32nd minute.

• ABenjamin is closer to home at 16 minutes than at 12 minutes after the start.
• BBenjamin is closer to home at 16 km than at 12 km after the start.
• CBenjamin is farther away from home at 16 minutes than at 12 minutes after the start.
• DBenjamin is farther away from home at 16 km than at 12 km after the start.

• AAt time , Benjamin is 1.2 km from home.
• BAt time 1.2 minutes, Benjamin is km from home.
• CAt time 1.2 minutes, Benjamin is km from home.
• DAt time , Benjamin is 2.4 km from home.

• AAfter minutes, Benjamin is 26 km from home.
• BAfter 13 minutes, Benjamin is km from home.
• CAfter minutes, Benjamin is 13 km from home.
• DAfter 13 minutes, Benjamin is km from home.

Q18:

You put a sweet potato, that has been left on the side in the kitchen, in the oven. After 45 minutes, you take it out. Let be the temperature of the potato minutes after you placed it in the oven. Rewrite each of these statements using function notation.

As you put the potato in the oven, the room temperature was 20.

• A
• B
• C
• D
• E

The potato was hotter at 10 minutes than at 5.

• A
• B
• C

The potato was at the same temperature at 40 minutes as it was when taken out.

• A
• B
• C

Q19:

Find , if and , .

Q20:

The function is given by the greatest integer that is less than or equal to . Which of the following is not true of this function?

• AThe range of is the set of all integers.
• B
• CThe domain of is assumed to be the set of all real numbers.
• D
• E

Q21:

Using the graph shown which represents the function , evaluate . • A0
• B
• C
• Dundefined

Q22:

The given graph represents a function. What would be the value of the output for an input of 5? Q23:

If the following graph represents the function , determine . Q24:

Find the output, , of the function represented by the given graph when its input is 2. Q25:

If the following graph represents the function , determine . 