SME
Grade 9 Math · Algebra 1
Function notation, domain and range, key features of graphs and average rate of change
Use this for “f(x) = 3x − 2. Find f(4), or the x that makes f(x) = 10.”
Chart
y-intercept (0, −2)
f(4) = 10
This is an example. Type your own values to start a new problem.
f(x)
=
m
x
+
(
b
)
f(
)
=
y
Formulas
y
=
m
×
x
+
b
10 = 3 × 4 + (−2)
Assumptions
•
f(x) is the output for input x, not f times x.
•
f(4) = 10 means the point (4, 10) is on the graph.
•
To solve f(x) = 13, set the rule equal to 13 and solve for x.
Step-by-step
WE KNOW
x = 4, m = 3, b = −2
FIND
output f(x) (y)
Step 1 · Find output f(x): y
Use y = m × x + b
Put
the
input
in
for
x
:
multiply
by
the
slope,
then
add
b
.
y
=
3
×
4
−
2
y
=
12
−
2
y
=
10
Check
Put the numbers back in. Both sides should match.
10 = 3 × 4 − 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
More problem types
Evaluate a quadratic
Use this for “f(x) = 2x² − 3x + 1. Find f(−2).”
Domain and range
Use this for “f(x) = −2x + 5 for −1 ≤ x ≤ 4. What is its range?”
Average rate of change
Use this for “Find the average rate of change of f(x) = x² − 4x + 1 from x = 1 to x = 4.”
Transform a function: g(x) = a·f(x − h) + k
Use this for “f(x) = x². Graph g(x) = 2f(x − 3) + 1. Where does the point (1, 1) of f go?”