IB AA · 3A Concepts of a Function
A function gives exactly one output for each allowed input.
Vertical line test
If a vertical line meets the graph more than once, y is not a function of x.
Equations
A rule with ±, or an equation that leaves y squared, usually gives two outputs.
One branch
y = keeps the nonnegative root only, so it is a function on its domain.
Points
In a table or a scatter, look for a repeated x with two different y-values.
Straight lines, a V, and a circle.
A function gives one output for each allowed input.
Every vertical line meets the graph once, so y is a function of x.
Yes. It is a function.
Answer: Yes. It is a function.
A function gives one output for each allowed input.
Each x has one y, so this is a function.
Yes. It is a function.
Answer: Yes. It is a function.
A function gives one output for each allowed input.
Each x has one y, so this is a function.
Yes. It is a function.
Answer: Yes. It is a function.
A function gives one output for each allowed input.
Each x has the same single output, so this is a function.
Yes. It is a function.
Answer: Yes. It is a function.
A function gives one output for each allowed input.
No two points share an x-coordinate, so this is a function.
Yes. It is a function.
Answer: Yes. It is a function.
A function gives one output for each allowed input.
A vertical line near the middle meets the circle twice, so this is not a function.
No. It is not a function of x.
Answer: No. It is not a function of x.
Curves that pass or fail the vertical line test.
A function gives one output for each allowed input.
A vertical line to the right of the vertex meets the graph twice, so y is not a function of x.
No. It is not a function of x.
Answer: No. It is not a function of x.
A function gives one output for each allowed input.
For x greater than 0, there are two y-values. This is not a function.
No. It is not a function of x.
Answer: No. It is not a function of x.
A function gives one output for each allowed input.
One x-value has many y-values, so this is not a function of x.
No. It is not a function of x.
Answer: No. It is not a function of x.
A function gives one output for each allowed input.
The curve wiggles, but each x still has only one y. It is a function.
Yes. It is a function.
Answer: Yes. It is a function.
A function gives one output for each allowed input.
x = 0 has two outputs, 3 and −2, so this is not a function.
No. It is not a function of x.
Answer: No. It is not a function of x.
The ± sign gives two outputs for each x greater than −4.
For example, x = 0 gives y = 2 and y = −2.
No. It is not a function of x.
Answer: No. It is not a function of x.
Decide from the equation.
y = is the same as y = |x|.
Each x has one output.
Yes. It is a function.
Answer: Yes. It is a function.
Cube each input. One input gives one output.
Yes. It is a function.
Answer: Yes. It is a function.
For each allowed x there is one value of the fraction.
Yes. It is a function. x = 0 is not in the domain.
Answer: Yes. It is a function.
y = ±.
Most x-values give two y-values.
No. It is not a function of x.
Answer: No. It is not a function of x.
The symbol keeps the nonnegative root only.
Each allowed x has one output.
Yes. It is a function.
Answer: Yes. It is a function.
Every point on this graph has x = 3, and y can be any real number.
One input has many outputs.
No. It is not a function of x.
Answer: No. It is not a function of x.
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