Inverse Functions
Find the inverse of the Relation:
{(-8,3),(-4,2),(0,1),(3,0),(5,-3),(9,-9)}
What is {(-9,9),(-3,5),(0,3),(1,0),(2,-4),(3,-8)} ?
Write the Domain & Range in interval notation of the function:
f(x)= -(√(x-1))+2
What is
Domain: [1,∞)
Range: (-∞,2] ?
Using Desmos, write the Domain & Range in interval notation of the function:
f(x)= |x-4|-3
What is
Domain: (-∞,∞)
Range: (-∞,-3] ?
Write the function in Standard Form, and Classify by Degree, then by number of terms.
f(x)= -4x+3x3-x5-8
What is
Standard Form: f(x)= -x5+3x3-4x-8
Classify by Degree: Quintic
Classify by Terms: Polynomial ?
Using Desmos, solve the system of equations by graphing.
y = -1/2(x2)-5x -4
y = -3/4(x)-2
What is Two Solutions: (-8,4) and (-1/2, -13/8) ?
Find the inverse of f(x)=(2x+3)/5
What is f-1(x)=(5x-3)/2 ?
WITHOUT using Desmos, fill in the blanks:
The function f(x)= √(x-3)+6 is vertically translated ___ units ______, and horizontally translated __ units to the ______.
What is
"6" and "Up"
"3" and "Right" ?
WITHOUT using Desmos, fill in the blanks:
The function f(x)=|x-7|-5 is vertically translated ___ units ______, and horizontally translated __ units to the ______.
What is
"5" and "Down"
"7" and "Right" ?
Determine whether the polynomial function is: Odd or Even Degree? Its End Behavior? Its "a" positive or negative?
f(x)=7x4-4x3+x2-5x-10
What is
Even Degree
As x approaches -∞, the y goes up. As x approaches ∞, the y goes up, as well.
"a" is positive ?
Using Desmos, solve the system of equations.
4x - y = -8
x + 4 = 2y
What is One Solution: (-12/7, -40/7) ?
Find the inverse of f(x)=-(x+3)2+3
What is f-1(x)=√(x-3)-3 ?
Using Desmos, tell me the horizontal and vertical translation of the function: *(-7,-3) is our endpoint
y=√(x+7)-3
What is
Horizontal Translation: 7 units to the Left
Vertical Translation: 3 units Down ?
Using Desmos, just tell me the horizontal and vertical translation of the function: *(5,-1/3) is our vertex
y=-(2/3)*|x-5|-(1/3)
What is
Horizontal Translation: 5 units to the Right
Vertical Translation: 1/3 units Down ?
If a quintic function crosses the x-axis at 1 point, but a quadratic function crosses the x-axis at 2 points, which function has the most real zeros?
What is The Quadratic Function ?
Using Desmos, solve the system of equations.
y = -x2+3x-2
y = x2-2x+3
What is NO Solution ?
(These do not intersect)
Are these inverses of one another?
f(x)= 2*√(3x) + 7
g(x)= (x2-14x+49)/6
What is
No, they are not inverses of one another ?
WITHOUT using Desmos, is the dilation done on this equation a vertical stretch or a vertical compression?
f(x)=6/4*√(x)+1
What is Vertical Stretch ?
Using Desmos, what are the transformation done to this function?
f(x)=2|x|-2
What is Vertical Stretch by a factor of 2, and Vertically Shift 2 units down ?
Using Desmos, find the following for f(x)= -x3-3x2+7
Local Min & Max?
What is
Local Min: 3
Local Max: 7 ?
Using Desmos, how many solutions will the system of equations have?
x2+y2=9
3y2=27-3x2
What is Infinite Solutions ?
(The functions are the exact same as one another.)
Show that these functions are the inverse of one another.
f(x)= (√(x-5))/3
g(x)= 9x2+5
What is When worked out completely, f(x)=g-1(x) and g(x)=f-1(x) ?
WITHOUT using Desmos, write the equation of a radical function that has been vertically compressed by 3 units, horizontally translated 4 units to the right, vertically translated 1 unit down, and is reflected over the x-axis.
What is f(x)= -1/3*√(x-4)-1 ?
WITHOUT using Desmos, write the equation of an absolute value function that has been vertically compressed by 4 units, horizontally translated 1 unit to the left, vertically translated 3 units up, and is reflected over the x-axis.
What is f(x)= -1/4*|x+1|+3 ?
Using Desmos, find the following for f(x)= -x3-3x2+7
Intervals of Increase & Decrease?
Domain & Range?
What is
Interval of Increase: (-2,0)
Interval of Decrease: (-∞,-2)U(0,∞)
Domain: (-∞,∞)
Range: (-∞,∞) ?
Using Desmos, write the how many solutions the system of equations has:
x2+y2=25
-x2=y2-36
What is No solutions ?
(These circles do not intersect)