Interpreting Equations
What does the number 5 in the equation represent?
g(x) = (x - 5)2
Horizontal shift to the right 5 units
Display graph f(x) = x2 in red and g(x) = -x2 in blue.
Name the transformation that takes the red graph to the blue graph
reflection over the x-axis
Give the name and equation for the parent function of
g(x) = 5(x-2)2-3
Quadratic function
f(x) = x2
Write an equation for the following function vertically stretched by a factor of 4,
g(x) = x4
h(x) = 4x4
How can you determine if a rule is a function?
The vertical line test -or-
no single input can have multiple outputs
Describe in words and in order all of the transformations on f(x) in order to get g(x).
g(x) = - f(x - 2) - 3
shift right 2, reflect over the x-axis, shift down 3
What is the equation for this graph?
Display graph f(x) = (x + 3)2 + 2
f(x) = (x + 3)2 + 2
Display the graph of f(x) = |x|
Name this parent function and give the equation
Absolute value function
f(x) = |x|
Write the general rule for a function f(x) reflected across the x-axis and for a function g(x) reflected across the y-axis
reflected across x-axis: -f(x)
reflected across y-axis: g(-x)
Let f(x) = (⅓)x3 + 7x
Evaluate f(-5)
-230/3
Which of the following functions have a vertical shift?
(a) f(x) = x3 - 5
(b) g(x) = 1/(x+2)
(c) h(x) = 7 - 3(x+1)2
(a) and (c)
Graph the function,
h(x) = |4x| + 2
Display graph of h(x) = |4x| + 2
Give the equation and graph the reciprocal function
f(x) = 1/x
Write an expression for g(x) vertically shrunk by a factor of 4 and reflected over the x-axis
-(1/4)g(x)
Let h(x) = 3x4 - 4
Evaluate h(2a)
h(2a) = 48a4 - 4
Describe in words all of the transformations on f(x) in order to get h(x).
h(x) = f(-2x) + 1
horizontal shrink by a factor of 2, reflect over y-axis, shift up 1
y = 2√(x+4) in blue.
Horizontal shift to the left 4, vertical stretch by a factor of 2
Give the equations for any asymptotes of the parent function:
f(x) = 1/x
H.A: y = 0
V.A: x = 0
Let f(x) = x2. Write the equation for g(x) where g(x) is f(x) reflected over the x-axis, stretched horizontally by a factor of 2, and shifted up 3 units.
g(x) = -[(1/2)x]2 + 3
Find where the following graph crosses the x-axis:
g(x) = x2 - 2x - 35
(7, 0) and (-5, 0)
Let g(x) = x3. List all of the transformations applied to g(x) in order to obtain f(x) = -(3x+6)3-2
horizontal shrink by a factor of 3, shift left 2, reflect over x-axis, shift down 2
Graph the equation
g(x) = 3(x - 1)3 + 2
Display graph of g(x) = 3(x - 1)3 + 2
Given the function:
f(x) = 5√(3x+7) -10
Name the parent function and graph the parent function
Square root function
Write an equation that takes the function,
f(x) = 2(x + 2)2 + 1
and translates it 3 units the left and 5 units down.
g(x) = 2(x + 5)2 - 4
Let p(x) = 2x and h(x) = x4 + 7
Evaluate (h○p)(4)
(h○p)(4) = 4103