ILEARN CHECKPOINT: LINEAR VS NONLINEAR

ILEARN
CHECKPOINT 2

LINEAR VS NONLINEAR
&
WHAT IS A FUNCTION?

Multiple Choice

Linear or nonlinear?

• linear
• nonlinear

Multiple Choice

Linear or nonlinear?

• linear

• nonlinear

Multiple Choice

Linear or nonlinear?

• linear

• nonlinear

Multiple Select

To determine if a table is a linear function, I need to

• Use the vertical line test.

• Check $$\frac{change\ in\ y}{change\ in\ x}$$

  This rate of change must be the same.

• Make sure the table starts at 0.

• Look for the initial value.

Multiple Choice

Is the function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is this table showing a linear or nonlinear function?

• Linear, the slope/ROC is constant

• Nonlinear, the slope/ROC is not constant

Match

Match the following

Linear; x is in the numerator, m=1/3

Nonlinear; x is in the denominator

nonlinear; x has an exponent

Linear; x is in the numerator, m=-2/5

nonlinear; taking the square root of x

• Linear; x is in the numerator, m=1/3

• Nonlinear; x is in the denominator

• nonlinear; x has an exponent

• Linear; x is in the numerator, m=-2/5

• nonlinear; taking the square root of x

PART TWO
FUNCTIONS

• In a coordinate (X, Y), the X-VALUES of a functions cannot repeat.

• The y-values really do not matter!

• HINT

  • -3 and 3 are two different numbers! This would not mean that "3" repeats.

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WHEN ARE COORDINATES FUNCTIONS?

​WHICH OF THE FOLLOWING COORDINATE SETS IS NOT A FUNCTION?
​A: (1, 2), (2, 3), (3, 4), (4, 5)
​B: (-1, -1), (0, 0), (1, 1), (2, 2)
​C: (1, 2), (1, 3), (1, 4), (1, 5)

Multiple Choice

Which relation is NOT a function?

• {(1,-5), (3,1), (-5,4), (4,-2)}

• {(2,7), (3,7), (4,7), (5,8)}

• {(1,-5), (-1,6), (1,5), (6,-3)}

• {(3,-2), (5,-6), (7,7), (8,8)}

Multiple Choice

Find the set of ordered pairs that is a function.

• A

• B

• C

• D

• Tables are the same as coordinates. The X-VALUES cannot repeat.

• The x column is always FIRST in a table. Either on the left or at the top.

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WHEN ARE TABLES FUNCTIONS?

x​	​	​	​	​
​y	​	​	​	​

​x	​y
​	​
​	​
​	​
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Multiple Choice

Function or not?

• Function
• Not a Function

Multiple Choice

Function or not?

• Function
• Not a Function

Multiple Choice

Is this table of values a function or not a function?

• Function

• Not a Function

• Mapping diagrams are the same as coordinates and tables. The X-VALUES cannot repeat.

• However, mapping diagrams use lines. Therefore, we do not want to see more than one line coming from an x-value & no repeating x's.

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WHEN ARE MAPPING DIAGRAMS FUNCTIONS?

Multiple Choice

Function or not?

• Function
• Not a Function

Multiple Choice

Function or not?

• Function
• Not a Function

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

• For all functions, the same rule holds true. The X-VALUES cannot repeat. Every x can only have one y.

• To tell this on a graph, we use the vertical line test.

  • There must be nowhere on the graph that you can draw a vertical (up and down) line and it intersect your graph more than once.

    • Doesn't intersect more than once = FUNCTION

    • Does intersect more than once= NOT A FUNCTION

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WHEN ARE GRAPHS FUNCTIONS?

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Function or not?

• Function
• Not a Function

Multiple Choice

Look at the graph. Is the relation a function?

• yes

• no

Multiple Choice

Does the graph represent a function?

• Yes, because the vertical line test shows there are no repeating input values
• No, because the vertical line test shows there are repeating input values

Multiple Choice

Function or not?

• It is a function because no vertical lines hit it twice.
• It's not a function because a vertical line hits it twice.
• It's not a function because no vertical lines hit it twice.
• It is a function because a vertical line hits it twice.