Evaluating & Composition
If f(x) = x + 6, find f(4).
→ 10
True or False: every relation is a function.
→ False
What does slope measure?
→ Rate of change / steepness ("rise over run")
What is the set of all inputs x values, of a relation called
domain
In y = mx + b, what does b represent in a cost function?
The starting/base fee
If h(x) = 2x − 3, find h(−2).
→ −7
What's the domain of f(x) = 1x, in words?
→ All reals numbers
Find the slope through (0, 2) and (4, 10).
→ m = 2
What is the set of all outputs called?
→ Range
A cab charges $3 base + $2/mile. Write the cost function C(m).
→ C(m) = 2m + 3
If f(x) = x² and g(x) = x − 1, find f(g(3)).
→ f(2) = 4
l(x) = 3 − x has domain . Find the range.
→ (1, 4)
Write the point-slope equation for slope −3 through (1, 4).
→ y = −3(x − 1) + 4
What does f(x) mean, in words?
→ The output of f when the input is x
Using C(m) = 2m + 3, find the cost for an 8-mile ride.
→ $19
If g(x) = 4x + 1, find [g(x+h) − g(x)] / h.
4
l(x) = 2x + 1 has domain [0, 3]. Find the range.
[1, 7]
Is {(2,3), (2,5), (4,7)} a function?
Why or why not? → No — input 2 has two different outputs
Simplify: x³y⁻² ÷ (x⁻¹y⁴)
Answer: x⁴/y⁶