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Wize Grade 11 Mathematics Textbook > Introduction to Functions

Basic Graphs

Review of Quadratic EquationsPrevious Section
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Basic Graphs

Some of the most common equations include linear, quadratic, square root, reciprocal, and absolute value equations.

Linear

  • Linear equations have the basic shape of a completely straight line.
  • The most basic of linear equations is y=xy=x.


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Quadratic

  • Quadratic equations have a distinctive u-shape.
  • The most basic of quadratic equations is y=x2y=x^2.


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Square Root

  • Square root equations increase as you read them from left to right.
  • The most basic of the square root equations is y=xy=\sqrt{x}.



Wize Tip
The value of the square root is defined for positive numbers. Because of this there is no graph on the left side when xx is negative.

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Reciprocal

  • Reciprocal equations involve dividing by the variable x.
  • The most basic of these is the equation y=1xy=\frac{1}{x}.




Wize Tip
Since we can not divide by zero, there is no value on the graph when x=0x=0.

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Absolute Value

  • The absolute value works by taking in a number and making it positive.
  • This gives absolute value equations a distinctive v-shape.
  • The most basic absolute value equation is y=∣x∣y=|x|.




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Example: Basic Graphs

What family of equations does the basic graph or table come from?

1.

Reciprocal

2.
Linear

3.

Quadratic

4.
Absolute Value

5.

Square Root

Practice: Basic Graphs

Match the graph with its equation.
A.
B.
C.
D.
E.
y=xy=x
y=x2y=x^2
y=∣x∣y=|x|
y=xy=\sqrt{x}
y=1xy=\frac{1}{x}

Practice: Basic Graphs

Of the five basic graphs covered, which one does not have a value when x=0x=0?

Practice: Basic Graphs

Of the five basic graphs covered, which one goes through the point (−1,1)(-1,1)?

Practice: Basic Graphs


The following graphs are related to the basic equations. Look at their distinctive features and match them with the family of equations they are related to.
A.
B.
C.
D.
Absolute Value
Quadratic
Square Root
Reciprocal

Basic Graphs

This reference sheet is super helpful for this course. Make sure to either create or print a copy of it to keep with you.