Functions flashcards
46 practice cards drawn from the Functions lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Functions lessons in full →
f(x) = 5x + 1. What is f(8)?
41
from “Function Notation”
f(x) = 5x + 6. What is f(5)?
31
from “Function Notation”
. Which input is not allowed?
6
from “Domain and Range”
. What is the smallest output?
9
from “Domain and Range”
f(x) = 4x + 1 for x < 5, and 14 − x for . What is f(5)?
9
from “Piecewise Functions”
f(x) = 3x + 1 for x < 2, and 10 − x for . What is f(4)?
6
from “Piecewise Functions”
f(x) = x + 1 for x < 2, and 7 − x for . Does the graph break at x = 2?
yes, it jumps
from “Graphing a Piecewise Function”
f(x) = x + 1 for x < 3, and 8 − x for . What is the filled endpoint?
(3, 5)
from “Graphing a Piecewise Function”
f(x) = 3x for x < 2, and x + k for . Which k joins the pieces?
4
from “Making a Piecewise Function Continuous”
f(x) = 5x for x < 5, and x + k for . Which k joins the pieces?
20
from “Making a Piecewise Function Continuous”
f(x) = x + 2, g(x) = 3x. What is gf(4)?
18
from “Composite Functions”
f(x) = x + 6, g(x) = 4x. What is gf(3)?
36
from “Composite Functions”
f(x) = 4x + 7. What is the inverse?
from “Inverse Functions”
f(x) = 3x + 8. What is the inverse?
from “Inverse Functions”
. Which way does the curve move?
5 up
from “Transforming Graphs”
. Which way does the curve move?
2 right
from “Transforming Graphs”
y = f(x) has a lowest value of 9. What is the lowest value of y = 2f(x)?
18
from “Stretching a Graph Vertically”
(1, 6) is on y = f(x). Where is it on y = 2f(x)?
(1, 12)
from “Stretching a Graph Vertically”
y = f(x) crosses the x-axis at x = 9. Where does y = f(3x) cross?
x = 3
from “Stretching a Graph Horizontally”
Which one squashes the graph of y = f(x) toward the y-axis?
y = f(5x)
from “Stretching a Graph Horizontally”
What is log base 10 of 10000?
4
from “Exponentials and Logarithms”
What is log base 2 of 16?
4
from “Exponentials and Logarithms”
3 multiplied by 2, 4 times over
48
from “Exponential Growth”
3 multiplied by 2, 3 times over
24
from “Exponential Growth”
64 halved 3 times
8
from “Exponential Decay”
48 halved 2 times
12
from “Exponential Decay”
After n half-lives, what fraction of a sample remains?
from “Growth and Decay Problems”
A colony of 100 bacteria doubles every hour. How many after 3 hours?
800
from “Growth and Decay Problems”
Which model stops growing at a ceiling?
from “Logistic Growth and Carrying Capacity”
. What is the carrying capacity?
125
from “Logistic Growth and Carrying Capacity”
log 20 − log 4 = log ?
5
from “The Laws of Logarithms”
log 4 + log 5 = log ?
20
from “The Laws of Logarithms”
Which quotient computes ?
from “The Change of Base Rule”
What is , exactly?
from “The Change of Base Rule”
ln undoes which function?
from “The Natural Logarithm”
What is ?
3
from “The Natural Logarithm”
. What is x?
3
from “Solving Exponential Equations”
. Which expression gives x?
from “Solving Exponential Equations”
What is ?
3
from “Logarithmic Graphs”
What is ?
3
from “Logarithmic Graphs”
Why take logs of growth data at all?
a line’s rule can be read off
from “Straightening Growth with Logarithms”
On the log plot of , what does the slope give?
log b
from “Straightening Growth with Logarithms”
A log-log line has slope 2 and intercept 0.7. Which model fits?
from “Straightening a Power Law”
On the log-log plot of , what does the slope give?
n
from “Straightening a Power Law”
Plotted against ln x the data give the line y = 5·(ln x) + 6. What is the model?
y = 6 + 5 ln x
from “Fitting a Logarithmic Model”
Values rise forever, but each extra unit of x adds less. Which model?
y = a + b ln x
from “Fitting a Logarithmic Model”