The rules that solve most questions
- Substitute first, then follow the order of operations: parentheses, exponents, multiplication, addition.
- In f(x) = a·bˣ, a is the starting value and b is the growth factor (b > 1 grows, 0 < b < 1 decays).
- Growth by r percent per period means multiplying by (1 + r/100) each period.
- In vertex form (x − h)² + k, the vertex is at (h, k).
Traps the wrong answers are built on
- Multiplying a·b before applying the exponent.
- Getting the sign of h wrong in (x + 4)², where h = −4.
Worked example
The function g is defined by g(x) = (x − 3)² − 2. What is the value of g(4)?
- A. 47
- B. 5
- C. 3
- D. −1
Answer: D. Substitute x = 4: g(4) = (4 − 3)² − 2. Inside the parentheses: 1. Squared: 1. Then 1 − 2 = −1.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Medium
The function g is defined by g(x) = (x − 3)² − 2. What is the value of g(4)?
Show answer and explanation
Answer: D
Substitute x = 4: g(4) = (4 − 3)² − 2.
Inside the parentheses: 1. Squared: 1.
Then 1 − 2 = −1.
- Question 2Medium
The function g is defined by g(x) = (x − 5)² − 3. What is the value of g(3)?
Show answer and explanation
Answer: D
Substitute x = 3: g(3) = (3 − 5)² − 3.
Inside the parentheses: −2. Squared: 4.
Then 4 − 3 = 1.
- Question 3Medium
The function g is defined by g(x) = (x + 4)² + 1. What is the value of g(2)?
Show answer and explanation
Answer: A
Substitute x = 2: g(2) = (2 + 4)² + 1.
Inside the parentheses: 6. Squared: 36.
Then 36 + 1 = 37.
- Question 4Easier
The function f is defined by f(x) = 7·4^x. What is the value of f(4)?
Show answer and explanation
Answer: A
Substitute x = 4: f(4) = 7 · 4^4.
4^4 = 256, so f(4) = 7 · 256 = 1792.
A common mistake is multiplying first: (7·4)^4 = 614656. Exponents are applied before multiplication.
- Question 5Easier
The function f is defined by f(x) = 9·2^x. What is the value of f(2)?
Show answer and explanation
Answer: C
Substitute x = 2: f(2) = 9 · 2^2.
2^2 = 4, so f(2) = 9 · 4 = 36.
A common mistake is multiplying first: (9·2)^2 = 324. Exponents are applied before multiplication.
- Question 6Easier
The function f is defined by f(x) = 5·4^x. What is the value of f(4)?
Show answer and explanation
Answer: D
Substitute x = 4: f(4) = 5 · 4^4.
4^4 = 256, so f(4) = 5 · 256 = 1280.
A common mistake is multiplying first: (5·4)^4 = 160000. Exponents are applied before multiplication.
- Question 7Medium
The function g is defined by g(x) = (x + 2)² + 7. What is the value of g(−1)?
Show answer and explanation
Answer: C
Substitute x = −1: g(−1) = (−1 + 2)² + 7.
Inside the parentheses: 1. Squared: 1.
Then 1 + 7 = 8.
- Question 8Medium
The function g is defined by g(x) = (x + 2)² − 5. What is the value of g(−1)?
Show answer and explanation
Answer: B
Substitute x = −1: g(−1) = (−1 + 2)² − 5.
Inside the parentheses: 1. Squared: 1.
Then 1 − 5 = −4.
- Question 9Medium
The function g is defined by g(x) = (x − 4)² + 6. What is the value of g(−3)?
Show answer and explanation
Answer: C
Substitute x = −3: g(−3) = (−3 − 4)² + 6.
Inside the parentheses: −7. Squared: 49.
Then 49 + 6 = 55.
- Question 10Easier
The function f is defined by f(x) = 6·3^x. What is the value of f(4)?
Show answer and explanation
Answer: C
Substitute x = 4: f(4) = 6 · 3^4.
3^4 = 81, so f(4) = 6 · 81 = 486.
A common mistake is multiplying first: (6·3)^4 = 104976. Exponents are applied before multiplication.
More Advanced Math practice
Questions people ask
Is this nonlinear functions practice like the real SAT?
The questions follow the format of the digital SAT's Advanced Math domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Advanced Math is one of the four content domains of the SAT Math section, alongside Algebra, Problem-Solving and Data Analysis, Geometry and Trigonometry.