Question

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1) Is the function described by the points in this table linear or nonlinear?

x y
−2 4
0 8
1 10
2 12
3 14

a)linear

b)nonlinear

2) Which table could be a partial set of values for a linear function?

x y
0 0
1 2
2 8
3 18


x y
0 3
1 5
2 7
3 9


x y
0 9
1 8
2 5
3 0


x y
0 1
1 2
2 5
3 10

3) Is this function linear or nonlinear?

y=2x2−4

a)nonlinear

b)linear

4)Select linear or nonlinear to correctly classify each function.
Function Linear Nonlinear
72=x3+y
y+1=5(x−9)
7y + 2x = 12
4y = 24

5) A function is represented by the values in the table.

x y
22 26
20 22
16 20
14 18
10 14
Choose from the drop-down menu to complete the statement.
The function represented in the table linear

a)is
b) is not

Answer 1

1)

Answer

a) linear

Explanation

There is a simple way to tell if a function is linear from a table: look at the x and y-values; if the y-values are increasing or decreasing by the same amount when their corresponding x-values increases or decreases by the same amount, you have a linear function; otherwise, you don't.

Look at the table

From 0 to 1 x is increasing by 1; from 8 to 10 (the corresponding values), y is increasing by 2

From 1 to 2 x is increasing by 1; from 10 to 12, y is increasing by 2

So, every time that x increases by 1, y increases by 2; therefore, we have a linear function.

Notice that form -2 to 0 x is increasing by 2; from 4 to 8 increasing by 4, which is the same rate as before (when x increases 1, y increases 1)

2)

Answer

x y

0 3

1 5

2 7

3 9

Explanation

When x increases by 1, y increases by 2; therefore we have a linear function.

If you look at the first and third tables,  y increases at different amounts every time x increases by 1; therefore, they are not linear functions.

In the first table when x increases by 1, y increases by 2, 4, or 10. Therefore, the table is not a linear function.

Similarly, in the third table when x increases by 1, y increases by 1, 3, or 5. Therefore, the table is not a linear function.

3)

Answer

a) nonlinear

Explanation

A linear function is function of the form: $y=mx+b$ or $Ay+Bx=C$ where $x$ is the independent variable and $y$ is the dependent variable.

In a linear function the coefficient of the variables is always 1.

Notice that the coefficient of the independent variable $x$, in the function $y=2x^2-4$, is 2; therefore the function is nonlinear.

4)

Answer

2=x3+y     Nonlinear

y+1=5(x−9)   Linear

7y + 2x = 12 Linear

4y = 24        Linear  

Explanation

2=x3+y The coefficient of the independent variable, x, is 3; therefore, the function is not linear.

y+1=5(x−9) We can simplify the expression to get:

y+1=5x-45

y=5x-46

Since y=5x-46 is in the form y=mx+b, we have a linear function.

7y + 2x = 12

Since 7y + 2x = 12 is a function of the form Ay + Bx = C, it is a linear function

4y = 24 We can siplify to get:

$y=\frac{24}{4}$

$y=6$

Since y=6 is a function of the form y = mx+b (with m=0), it is a linear function.

5)

Answer

b) is not

Explanation

From 22 to 20, x decreases by 2; from 26 to 22, y decreases by 4. So, when x decreases by 2, y decreases by 4.

From 16 to 14, x decreases by 2; from 20 to 18, y decreases by 2. So, when x decreases by 2, y decreases by 2.

When x decreases by 2, y decreases by 4 or 2; therefore the function represented in the table is not a linear function.