Functions & Notation
If f(x) = 3x² − 5x + 2, find f(2).
4
Simplify: (x²)(x³)
x⁵
What transformation occurs from y = x² to y = x² + 4?
Shift up 4 units.
What does slope measure?
Rate of change.
ΔY/ΔX
Simplify: e⁰
1
What does f(3) represent?
The output/value of the function when x = 3
Factor completely: x² − 9
(x − 3)(x + 3)
What is the slope of a horizontal line?
0
Find the average rate of change from x = 1 to x = 5 for f(x) = 2x.
2
What is the amplitude of this function 6sin(3x)+2?
6
If g(x) = √(x − 1), what is the domain (All Valid Values of X)?
x ≥ 1 or (1, ∞)
Simplify: (x² − 4)/(x − 2)
x + 2, where x ≠ 2
What is the slope of a Vertical Line?
Undefined
Find the slope between points (2, 5) and (6, 13).
2
Solve: 2^x = 8
What is x?
x = 3
A function passes the vertical line test. What does this mean?
Each x-value has exactly one y-value.
Solve for x: 2x² − 8 = 0
x = ±2
Describe the X and Y directions of a line with the equation of:
y = −x³.
As x → ∞, y → −∞ and as x → −∞, y → ∞
A car travels 180 miles in 3 hours. What is its average velocity?
60 mph
What is the period of sin(x)?
2π
If h(x) = 2x + 1 and k(x) = x², find (h (k (x)).
2x² + 1
Simplify: (2x²y³)(3xy²)
6x³y⁵
A line has slope −3 and passes through (1, 4). Write the equation.
y = −3x + 7
Find the average rate of change from x = 2 to x = 2.001 for f(x) = x3. (to 3 decimal places)
12.006
Rewrite: √(x³), using exponents.
x^(3/2)