Identify Functions

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Question 1 of 7

1. Question
Identify if the curve $x = y^{2}$ $x=y^2$ is a function
- 1. $Function$ $\text(Function)$
- 2. $Not a Function$ $\text(Not a Function)$
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There are two ways to check if an equation is a function: the algebraic method and the vertical line test

Method One: Algebraic Method

Substitute any value to $x$ $x$ and solve for $y$ $y$ . A function should have one value for $y$ $y$ for every value of $x$ $x$

$x$ $x$ $=$ $=$ $y^{2}$ $y^2$

$2$ $2$ $=$ $=$ $y^{2}$ $y^2$ Substitute $x = 2$ $x=2$

$\sqrt{2}$ $sqrt2$ $=$ $=$ $\sqrt{y^{2}}$ $sqrt(y^2)$ Find the square root of both sides

$\sqrt{2}$ $sqrt2$ $=$ $=$ $y$ $y$

$y$ $y$ $=$ $=$ $\pm \sqrt{2}$ $+-sqrt2$

$y$ $y$ has $2$ $2$ values $(\sqrt{2}, - \sqrt{2})$ $(sqrt2, -sqrt2)$ for one value of $x (2)$ $x (2)$ . Therefore, the equation is not a function

$Not a Function$ $\text(Not a Function)$

Method Two: Vertical Line Test

Draw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.

At $x = 2$ $x=2$ , the vertical line intercepts the curve line twice. Therefore, $x = y^{2}$ $x=y^2$ is not a function

$Not a Function$ $\text(Not a Function)$
Question 2 of 7

2. Question
Identify if the curve $y = 2^{x}$ $y=2^x$ is a function
- 1. $Not a Function$ $\text(Not a Function)$
- 2. $Function$ $\text(Function)$
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical line

Draw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.

The vertical line intercepts the curve line once. Therefore, $y = 2^{x}$ $y=2^x$ is a function

$\text(Function)$
Question 3 of 7

3. Question
Identify if the curve $x^2+y^2=9$ is a function
- 1. $\text(Function)$
- 2. $\text(Not a Function)$
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical line

Draw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.

The vertical line intercepts the curve line twice. Therefore, $x^2+y^2=9$ is not a function

$\text(Not a Function)$
Question 4 of 7

4. Question
Identify if the curve $y=sqrt(4-x^2)$ is a function
- 1. $\text(Function)$
- 2. $\text(Not a Function)$
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical line

Draw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.

The vertical line intercepts the curve line once. Therefore, $y=sqrt(4-x^2)$ is a function

$\text(Function)$
Question 5 of 7

5. Question
Identify if the curve is a function
- 1. $\text(Not a Function)$
- 2. $\text(Function)$
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical line

Draw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.

The vertical line intercepts the curve line once. Therefore, the curve is a function

$\text(Function)$
Question 6 of 7

6. Question
Identify if the curve is a function
- 1. $\text(Not a Function)$
- 2. $\text(Function)$
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical line

Draw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.

Notice that if the vertical line is drawn at this point, it intercepts both the empty circle (“less than/greater than” indicator) and the filled circle (“less than or equal/greater than or equal” indicator)

The empty circle is not included to the value of the curve, so the vertical line intercepts the curve only once. Therefore, it is a function

$\text(Function)$
Question 7 of 7

7. Question
Identify if the line is a function
- 1. $\text(Function)$
- 2. $\text(Not a Function)$
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical line

Since the curve itself is a vertical line, the value of $x (3)$ has all real values of $y$

The $x$ value should only have one $y$ value for it to be a function. Therefore, the curve is not a function

$\text(Not a Function)$

Identify Functions

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Quizzes

$x$ $x$	$=$ $=$	$y^{2}$ $y^2$
$2$ $2$	$=$ $=$	$y^{2}$ $y^2$	Substitute $x = 2$ $x=2$
$\sqrt{2}$ $sqrt2$	$=$ $=$	$\sqrt{y^{2}}$ $sqrt(y^2)$	Find the square root of both sides
$\sqrt{2}$ $sqrt2$	$=$ $=$	$y$ $y$
$y$ $y$	$=$ $=$	$\pm \sqrt{2}$ $+-sqrt2$