Functions revision

Functions revision

Functions

• Domain - x values (input)

• Range - y values (output)

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Multiple Choice

Is this mapping a function or not a function? 

• 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.

To test if something is a function, we use the vertical line test

Multiple Choice

Is this a function?

• Yes

• No

• Maybe

• I like circles

Multiple Choice

Is this a function?

• Yes

• No

• Maybe

• It's a curvy line

We write a function as

 $f\left(x\right)$  

We can also evaluate functions

 $f\left(x\right)=2x+3x^2$  

Find the value of  $f\left(2\right)$  
 $f\left(2\right)=2\left(2\right)+3\left(2\right)^2$  
 $f\left(2\right)=4+12$  
 $f\left(2\right)=16$  

Multiple Choice

• 27

• 21

• 24

• 72

Multiple Choice

• 8

• -24

• 24

• -22

Multiple Choice

• 24

• -6

• 32

• 36

A linear function is in the form

 $y=mx+c$  

 $m\ is\ the\ gradient$  
 $c\ is\ the\ y-intercept$  

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2
• 3
• 5
• Cannot be Determined 

Multiple Choice

What type of slope does the following graph have?

• Postive
• Negative
• Zero Slope
• Undefined

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Look at the graph.  Write down the equation for the line.

• y = - x + 3
• y = 4x + 3
• y = ¹/₄ x + 3
• y = - 4x + 3

Quadratic functions can be written as

 $y=ax^2+bx+c$  

Multiple Choice

Factorise: x² + 13x + 30

• (x + 3)(x + 10)

• (x + 5)(x + 6)

• (x + 2)(x + 15)

• (x + 1)(x + 30)

Multiple Choice

Factor: x² - 14x + 24

• (x + 2)(x - 14)

• (x - 2)(x - 12)

• (x + 14)(x - 2)

• (x - 4)(x - 6)

Multiple Choice

Factorise the expression...

5x² + 14x - 3

• (5x - 1)(x + 3)

• (5x - 3)(x + 1)

• (5x + 1)(x + 3)

• (5x - 1)(x - 3)

To sketch a quadratic function:

Find the y-intercept (make x = 0)

Find the x-intercepts (make y=0)

Determine if the quadratic is concave up or down

if the value of a>0 then it is positive, concave up

if the value of a<0 then it is negative, concave down

Find the vertex of the quadratic

Multiple Choice

What is another name for the x-intercepts and solutions of a quadratic?

• y-intercept

• Zeros

• x-axis

• They don't have another name

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Multiple Choice

Does the following graph have a maximum or minimum.

• Maximum
• Minimum

Multiple Choice

Use the picture to find the vertex and axis of symmetry

• Vertex (3,8) Axis x = 3

• Vertex (3,8) Axis y = 3

• Vertex (8,3) Axis x = 3

• Vertex (8,3) Axis y = 3

Multiple Choice

A parabola has a vertex at (-3,2).

What is the axis of symmetry?

• y = -2

• x = 3

• x = -3

• y = 2

Multiple Choice

What is the domain and the range for the graph?

• Domain : -2 ≤ x ≤ 2
  Range : 0 ≤ y ≤ 4
• Domain : 0 ≤ x ≤ 4
  Range : -2 ≤ y ≤ 2
• Domain : All real #s
  Range : y ≤ 4
• Domain : -2 ≤ x ≤ 2
  Range : y ≤ 4

Multiple Choice

Determine the domain and range of the function

• Domain: All real numbers

  Range: All real numbers

• Domain: x ≥ -4

  Range: All real numbers

• Domain: All real numbers

  Range: y ≥ -4

• Domain: -1 ≤ x ≤ 5

  Range: y ≥ -4

Transformations of functions

Multiple Choice

Describe the transformation that occurred

g(x) =2f(x)

• Up 2 units

• vertical compression

• vertical stretch

• Right 2 Units

Multiple Choice

Describe the transformation that occurred

k(x) = f(x) - 9

• vertical compression

• Down 9 units

• Left 9 units

• Right 9 Units

Multiple Choice

Describe the transformation that occurred.

w(x) = f(x - 7)

• Down 7

• Up 7

• Right 7

• vertical compression

Multiple Choice

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Strech

• right 2 units

Multiple Choice

Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Multiple Choice

What are the transformations?
y=(x-2)³+4

• Horz shift right 2      Vert shift up 4
• Horz shift left 2    Vert shift up 4
• Horz shift right 2      Vert shift down 4
• Horz shift left 2      Vert shift up 4

Multiple Choice

Describe the transformation from dotted to solid.

• f(x + 5) + 3
• f(x +3) + 5
• f(x - 5) + 3
• f(x - 3) + 5

Multiple Choice

Which of the equations best represents the transformation that occurred from the quadratic's parent function $y=x^2$  

•  $y=\left(x-2\right)^2-1$  

•  $y=\left(x+2\right)^2-1$  

•  $y=\left(x-2\right)^2+1$  

•  $y=\left(x+2\right)^2+1$  

Finished