Integrated Math 1 / Unit 3: Functions
3.4 Key Features of Graphs
Notes
Key features describe a function's graph and what it says about a situation.
- Intercepts: the $y$-intercept is where $x = 0$; an $x$-intercept is where $y = 0$.
- Increasing means the graph rises left to right; decreasing means it falls.
- A maximum or minimum is the highest or lowest output.
- Example: for $f(x) = 4x + 12$, set $4x + 12 = 0$ to get the $x$-intercept $x = -3$; $f(0) = 12$ is the $y$-intercept.
Practice
What is the $y$-intercept of $f(x) = 2x - 6$?
The $y$-intercept is $f(0) = -6$, the point $(0, -6)$.
What is the $x$-intercept of $f(x) = 4x + 12$?
Set $4x + 12 = 0$, so $4x = -12$ and $x = -3$.
A graph rises from left to right until $x = 2$, then falls. Which statement is true?
It goes up to $x = 2$ and then down, so the peak at $x = 2$ is a maximum.
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