Key features of a graph: intervals, extremes, end behavior and asymptotes
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
On a worksheet, f(x) = √x. Tala finds the average rate of change from x = 4 to x = 16. What is it?
In a notebook, Zee has f(x) = 3ˣ. What is its average rate of change from x = 0 to x = 2?
Ari works in pencil with f(x) = x³. What is the average rate of change from x = -1 to x = 3?
On a puzzle card, f(x) = 12/x. Bo needs the average rate of change from x = 1 to x = 4. What is it?
On a worksheet, f(x) = -2x³ + x. Esme describes the end of the graph. As x → ∞, what happens to f(x)?
- f(x) → ∞
- f(x) → -∞
- f(x) → 0
On a puzzle card, f(x) = 1/x + 2. Luz needs the end behavior as x → ∞. Which is it?
- f(x) → 2
- f(x) → 0
- f(x) → -∞
- f(x) → ∞
On a worksheet, f(x) = 3/(x − 2) + 1. Pia draws its asymptotes as dashed lines. Which are they?
- x = -2 and y = 1
- x = 2 and y = 1
- x = 1 and y = 2
- x = 2 and y = 3
In a notebook, Ren sketches f(x) = 2/(x + 4) − 3. What are its asymptotes?
- x = 4 and y = -3
- x = -4 and y = -3
- x = -3 and y = -4
- x = -4 and y = 2
Tala works in pencil with f(x) = log₂(x + 3). Which lines are its asymptotes?
- x = 3 only
- y = -3 only
- x = -3 only
- x = 0 only
On a puzzle card, f(x) = 5 · 2ˣ + 4. Zee needs its asymptotes. Which are they?
- y = 0 only
- x = 4 only
- y = 5 only
- y = 4 only