Representation using an equation of $X$ and $Y$

Question Types:

Representation using an equation of $X$ and $Y$

Representation using a graph, plotting on the $X$ and $Y$ axis

Representation using a table $X,Y$ of points on the graph

Expressing the relationship between $X$ and $Y$ using words

$Y=$ or $f(x)=$

Question 1

Determine whether the following table represents a function

Question 2

Is the given graph a function?

Question 3

Is the given graph a function?

Question 4

Is the given graph a function?

Question 5

Which of the following equations corresponds to the function represented in the graph?

Determine whether the following table represents a function

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can see that there is a constant change in the X values, specifically an increase of 2, and the Y value remains constant.

Therefore, according to the rule, the table describes a constant function.

Yes

Is the given graph a function?

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

We should note that for every X value found on the graph, there is one and only one corresponding Y value.

Therefore, the graph is indeed a function.

Yes

Is the given graph a function?

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

Let's note that in the graph:

$f(0)=2,f(0)=-2$

In other words, there are two values for the same number.

Therefore, the graph is not a function.

No

Is the given graph a function?

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

We should note that for every X value found in the graph, there is one and only one corresponding Y value.

Therefore, the graph is indeed a function.

Yes

Which of the following equations corresponds to the function represented in the graph?

Let's use the below formula in order to find the slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

We begin by inserting the known data from the graph into the formula:

$(0,-2),(-2,0)$

$m=\frac{-2-0}{0-(-2)}=$

$\frac{-2}{0+2}=$

$\frac{-2}{2}=-1$

We then substitute the point and slope into the line equation:

$y=mx+b$

$0=-1\times(-2)+b$

$0=2+b$

Lastly we combine the like terms:

$0+(-2)=b$

$-2=b$

Therefore, the equation will be:

$y=-x-2$

$y=-x-2$

Question 1

Which of the following equations corresponds to the function represented in the table?

Question 2

Determine whether the data in the following table represent a constant function

Question 3

Determine whether the following table represents a function

Question 4

Determine whether the following table represents a function

Question 5

Determine whether the following table represents a function

Which of the following equations corresponds to the function represented in the table?

We will begin by using the formula for finding slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

First let's take the points:

$(-1,4),(3,8)$

$m=\frac{8-4}{3-(-1)}=$

$\frac{8-4}{3+1}=$

$\frac{4}{4}=1$

Next we'll substitute the point and slope into the line equation:

$y=mx+b$

$8=1\times3+b$

$8=3+b$

Lastly we'll combine like terms:

$8-3=b$

$5=b$

Therefore, the equation will be:

$y=x+5$

$y=x+5$

Determine whether the data in the following table represent a constant function

No

Determine whether the following table represents a function

No

Determine whether the following table represents a function

Yes

Determine whether the following table represents a function

Yes

Question 1

Is the given graph a function?

Question 2

Is the given graph a function?

Question 3

Is the given graph a function?

Question 4

Is the given graph a function?

Question 5

Determine whether the following table represents a function

Is the given graph a function?

Yes

Is the given graph a function?

No

Is the given graph a function?

Yes

Is the given graph a function?

No

Determine whether the following table represents a function

No