Algebraic & Function Expressions

Solve Function Expressions

2019 December(C03) Math Question 1

Given that f(x) = 3x³ − 7, what is f(−2)?

2024 September(H11) Math Question 1

The function f is defined below. f(x) = |x|. What is(are) the output value(s) of f(2)?

2024 December(H31) Math Question 1

A function, f, is defined by f(x,y) = 3x² − 2y. What is the value of f(2,3)?

35 February(Z14) Math Question 2

4. Let the function f be defined as f(x) = 5x2 — 7(4x + 3). What is the value of f(3) ?

2017 April(74F) Math Question 4

6. A function, f, is defined by f(x,y) = 3Ã—2 â€” 4y. What is the value of f(4,3) ?

2018 June(A11) Math Question 6

2011 April(67F) Math Question 7

The function f(c) = (9/5)c + 32 gives the temperature, f(c) degrees Fahrenheit, that corresponds to c degrees Celsius. To the nearest 0.1°F, what Fahrenheit temperature corresponds to 13.0°C?

2024 June(G20) Math Question 7

7. The number of fish, f, in Skipper’s Pond at the beginning of each year can be modeled by the equation f (x) = 3(2x), where x represents the number of years after the beginning of the year 2000. For example, x = 0 represents the beginning of the year 2000, x = 1 represents the beginning of the year 2001, and so forth. According to the model, how many fish were in Skipper’s Pond at the beginning of the year 2006 ?

Exponential Equations

2021 April(Z04) Math Question 7

2011 June(69F) Math Question 9

9. If g(x) = 2x^2 — 3x + 4, then g(-3) = ?

2016 April(73E) Math Question 9

Which of the following equations gives a function f(x) that satisfies f(4) = 9?

2024 April(Z13) Math Question 9

10. If f(x) 3×2 + 7x — 8, then f(-3) = ?

2018 April(A09) Math Question 10

2010 June(68C) Math Question 10

2020 June(C02) Math Question 10

2009 April(66F) Math Question 11

2020 June(C02) Math Question 12

13. The population of a particular town is modeled by the equation P = 120,000(1.1)^t, where t is the number of years after January 1, 2011. Based on the model, which of the following numbers is closest to the population of the town on January 1, 2013 ?

2016 April(73E) Math Question 13

2009 June(67C) Math Question 14

The 7th term and the 8th term of an arithmetic sequence are 4 and 12, respectively. What is the 2nd term of this sequence?

2024 September(H11) Math Question 14

2012 April(70G) Math Question 16

2019 June(72F) Math Question 17

2013 April(71G) Math Question 18

18. The function f is defined as f(x) = —4x3 4x2. What is f(-4) ?

2015 June(73C) Math Question 18

2013 December(71E) Math Question 18

19. Cowling's rule is a method of calculating a medication dosage for a child by using the child's age and the adult dosage. The rule uses the formula d = a( t + 1 / 24 ), where d is the child's dosage in milligrams, a is the adult dosage in milligrams, and t is the child's age in years. Dato is taking a 150-milligram dosage of medication that has an adult dosage of 300 milligrams. According to this rule, which of the following values is closest to Dato's age in years?

2014 December(72G) Math Question 19

2009 June(67C) Math Question 19

Given f(x) = 2x − 5, what is the inverse, f⁻¹(x)?

2025 October(J08) Math Question 20

2012 June(70C) Math Question 21

2010 April(68G) Math Question 21

Given functions f(x) = 4x + 3 and g(x) = x² − 2, what is the value of f(g(−3))?

2024 June(G20) Math Question 21

2020 July(C01) Math Question 22

Given that h(z) = (−5z) + 8 and g(z) = −2z² + 2z + 8, what is (h + g)(z)?

2024 December(H31) Math Question 22

2012 December(71A) Math Question 24

The table below gives the values of 3 functions

2009 April(66F) Math Question 25

27. The isotope iodine-131 has a half-life of 8 days, which
means that .the amount of iodine-131 remaining after t -
t days is N½( ) 8, where N is the number of grams of
iodine-i31 at t = 0. How many grams of iodine~131
will remain after 16 days if there were 32 grams of
iodine-131 at t = 0 ?

2019 June(B02) Math Question 27

2020 July(C01) Math Question 28

2023 September(G01) Math Question 28

Given functions f(x) = 3x + 4 and g(x) = x² − 2, what is the value of f(g(−3))?

2024 April(Z13) Math Question 28

29. Given that 3(x − 2) = 6x − 3, what is the value of 9x − 2 ?

Solving equations

2021 April(D05) Math Question 29

29. Hikers’ World Foods sells raisin-nut mix in bulk to stores. The dollar amount per pound, P(x), for a store to purchase x pounds of raisin-nut mix from Hikers’ World is given by the function below. P(x) = 3.50 + 0.90x To the nearest $0.01, which of the following dollar values is equal to the total price for a store to purchase 100 pounds of raisin-nut mix in a single order from Hikers’ World?

Laws of exponents

2020 December(D03) Math Question 29

The concentration of a certain medication decreases each hour such that at t = 0 hours, the concentration is approximately equal to 850 mg/L; at t = 6 hours, the concentration is approximately equal to 151 mg/L; and at t = 12 hours, the concentration is approximately equal to 27 mg/L. One of the following identifies the best type of functional model for the data representing this 12-hour interval and gives a valid reason why that model is best. Which one?

2025 October(J08) Math Question 29

2011 June(69F) Math Question 30

Tables of values for the 2 functions f and g are shown below. What is the value of g(f(5))?

2024 September(H11) Math Question 31

Given f(x) = x + 2 and g(x) = 1/x², where x > 0, what is g(f(x))?

2024 December(H31) Math Question 32

The equation y = f(x) is graphed in the standard (x,y) coordinate plane below. One of the following defines f. f(x) = ?

2024 September(H11) Math Question 36

2009 December(68A) Math Question 38

38. Let the polynomial functions f and g be defined as f (x) = x2 + 7x − 3 and g(x) = x2 − 4x + 5. Let h(x) = f (x) − g(x). What is h(2) ?

Funny functions

2021 December(E23) Math Question 38

39. The operation ⊗ is defined on the set of positive integers by the rule a ⊗ b = a + b2. What is the value of (4 ⊗ 3) ⊗ 5 ?

2021 April(D05) Math Question 39

For f(x) = 2x + 3 and g(x) = x² − 4, which of the following expressions represents f(g(x))?

35 February(Z14) Math Question 39

Two functions, f and g, are defined over all real numbers by f(x) = 2x − 1 and g(x) = 3x² − 7. What is g(f(5x))?

2023 September(G01) Math Question 39

2019 April(B04) Math Question 40

2009 April(66F) Math Question 42

2020 July(C01) Math Question 45

46. Given g(x) = , which of the following expressions x- is equal to g(x — 1) for all x in its domain?

2016 December(74H) Math Question 46

The function f(x) = x⁵ is defined for all real numbers x. Which of the following expressions represents f⁻¹(x)?

35 February(Z14) Math Question 46

2020 July(C01) Math Question 49

Consider the graphs of the functions f(x) = (x + 2)(x − 8) and g(x) = x² + 5x − 12 in the standard (x,y) coordinate plane. What is the sum of the y-intercepts of the functions?

2023 April(F11) Math Question 51

2009 December(68A) Math Question 54

A 2nd tank has 30 gallons in it when its pump is turned on at t = 0 seconds. In terms of gallons of water moved over time, this pump behaves the same as the other pump. One of the following functions represents the volume, in gallons, of water in the 2nd tank t seconds after the pump is turned on. Which one?

2024 June(G20) Math Question 54

The function below is defined for constants a and b and for all positive integers n. r(n) = abⁿ. It is known that r(1) = 1/2, r(2) = 3/2, r(3) = 9/2, and r(4) = 27/2. Which of the following functions is equivalent to r(n)?

Solve Function ExpressionsAlgebraic & Function ExpressionsACT math questions

2019 December(C03) Math Question 1

2024 September(H11) Math Question 1