Algebra 2024 3.7 Lesson

​Bellwork

Multiple Choice

Which parent function matches the graph?

• y = |x|
• y = ∛(x)
• y = x²
• y = a⋅b^x

Multiple Choice

What type of function is shown?

• linear
• quadratic
• square root
• absolute value

Multiple Choice

What type of function is shown?

• Exponential 
• square root
• quadratic
• cube root

Multiple Choice

Which parent function matches the graph?

• f(x) = √(x)
• f(x) = ∛(x)
• f(x) = |x|
• f(x) = a⋅b^x

Multiple Choice

What type of function is shown?

• exponential
• linear
• quadratic
• square root

Multiple Choice

Which parent function matches the graph? 

• f(x) = x
• f(x) = x²
• f(x) =√(x)
• f(x) =∛(x)

Multiple Choice

Which parent function matches the graph? 

• f(x) = a⋅b^x
• f(x) = ∛(x)
• f(x) = √(x)
• f(x) = x²

Multiple Choice

Which of the following parent functions does not have a Domain of all Real numbers?

Multiple Choice

For $$y=a\left(x\ -\ h\right)^n+k$$ , how does adding a constant (k) transform the parent function?

• Horizontal shift

• Vertical Shift

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

For $$y=a\left(x\ -\ h\right)^n+k$$ , how does adding or subtracting an (h) value from x transform the parent function?

• Horizontal shift

• Vertical Shift

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

For $$y=a\left(x\ -\ h\right)^n+k$$ , What transformation happens when the a becomes negative?

• Horizontal shift

• Vertical Shift

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

For $$y=a\left(x\ -\ h\right)^n+k$$ , What transformation happens when the a is between 0 and 1

• Vertical stretch

• Vertical compression

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

For $$y=a\left(x\ -\ h\right)^n+k$$ , What transformation happens when the a is greater than 1

• Vertical stretch

• Vertical compression

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

If the blue function is f(x)=x², then the red function must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

  The blue function is the parent function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Multiple Choice

What is the equation of the graph below?

• f(x) = I x + 2 I 
• f(x) = I x + 2 I +2
• f(x) = I x - 2 I +2
• f(x) = I x - 2 I 

Multiple Choice

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1
• f(x) = (x + 2)² - 1
• f(x) = -(x + 2)² - 1
• f(x) = -(x - 2)² - 1

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated to the left one and down five.
• f(x) has been translated to the right one and down five.
• f(x) has been translated to the left one and up five.
• f(x) has been translated to the right one and up five.

Multiple Choice

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

• Reflect over y-axis
  Shifted down 10 units
  Shifted left 6 units
• Reflect over x-axis
  Shifted up 10 units
  Shifted left 6 units
• Reflect over y-axis
  Shifted up 10 units
  Shifted right 6 units
• Reflect over x-axis
  Shifted down 10 units
  Shifted left 6 units

Multiple Select

Describe the transformations from the graph of f to the graphs of g and h.

• The graph of g is a vertical translation 2 units down of the graph of f

• The graph of h is a horizontal translation 2 units right of the graph of f.

• The graph of g is a vertical translation 2 units up of the graph of f

• The graph of h is a horizontal translation 2 units left of the graph of f.

• The graph of g is a horizontal translation 2 units left of the graph of f

Multiple Select

Describe the transformations from the graph of f to the graphs of g and h.

• The graph of g is a vertical translation 1 unit up of the graph of f.

• The graph of h is a horizontal translation 1 unit left of the graph of f.

• The graph of g is a vertical translation 1 unit down of the graph of f.

• The graph of h is a horizontal translation 1 unit right of the graph of f.

• The graph of h is a vertical translation 1 unit down of the graph of f.

Multiple Choice

Describe the transformations from the graph of f to the graphs of g

• The graph of g is a reflection in the x-axis of the graph of f

• The graph of g is a reflection in the y-axis of the graph of f

Multiple Choice

Describe the transformations from the graph of f to the graphs of g

• The graph of g is a reflection in the x-axis of the graph of f

• The graph of g is a reflection in the y-axis of the graph of f

Multiple Choice

The table represents two linear functions f and g. Describe the transformation from the graph of f to the graph of g.

• The graph of g is a horizontal shift 4 units left of the graph of f

• The graph of g is a reflection of the graph of f across the x-axis.
• The graph of g is a vertical shift 4 units up of the graph of f.

• The graph of g is a vertical shrink of the graph of f by a factor of 1/4

Multiple Choice

1.    Considering the table below, describe the transformation in order to determine the value of the real number, 𝑘, that defines the transformation from 𝑓(𝑥) to 𝑔(𝑥).

• k = 4

• k = -4

• k = 1/4

• k = -1/4