Is It a Function?
Is the relation {(1, 2), (2, 3), (3, 4)} a function?
Yes. Each input has only one output.
If f(x)=2x+3, what is f(4)?
11
What does a linear function look like?
A straight line.
What’s the domain of f(x)=x2?
All real numbers.
What rule do we use on a graph to check if it’s a function?
Vertical Line TestNot a function — 2 maps to more than one output.
What does f(x) mean?
The output of function f for input x.
What does a nonlinear function do that a linear one doesn’t?
It curves; the rate of change isn't constant.
What’s the range of f(x)=x2?
All real numbers ≥ 0.
{(2, 3), (2, 5), (4, 6)} — function or not? Why?Describe how to fix a graph that fails the vertical line test.
Not a function — 2 maps to more than one output
Given f(x)=x2−4x, what is f(−1)?
5
A ball is thrown in the air. Sketch or describe the graph.
Parabola (arch shape)
From the table: x = {-1, 0, 2}; y = {1, 0, 4}. Give the domain and range.
Domain: {-1, 0, 2}; Range: {0, 1, 4}
Remove one of the y-values for the same x-value.
Describe how to fix a graph that fails the vertical line test.
Create your own function and find f(3).
Open ended
Is a taxi fare graph discrete or continuous? Why?
Discrete — charged by the mile, no partials.
Why is the domain of a real-world function sometimes limited?
You can't have negative time, miles, etc.