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Inverse Functions
Parent Functions and Transformations
Function Operations and Composition of Functions
Radical Functions
Polynomial Functions
100
The test that we use to see if a graph of a function will have an inverse.
What is Horizontal Line Test.
100
The equation and graph of the quadratic and cubic functions.
What is f(x)=x^2 and f(x)=x^3
100
f(x)= x^2 -2x and g(x)= 3x-4 (f+g)(x) and (f-g)(x) is…
What is (f+g)(x)= x^2 +x-4; (f-g)(x)= x^2 -5x+4
100
T/F When solving radical functions, the solutions we find will always work when substituted back into the original equation.
False. This is why we need to check our solutions.
100
The number of zeros a polynomial will have is the same number as the..
What is the degree/ highest power/ greatest exponent
200
The 5 steps we use to find the inverse of a function.
What is 1. graph/horizontal line test 2. substitute y for f(x) 3. switch x and y in your equation 4. solve for y 5. change y to f^-1(x).
200
The equation and graph of the reciprocal, square root, and absolute value functions.
What is f(x)= 1/x f(x)= square root of x f(x)=|x|
200
For f(x)= x^2 -2x and g(x)= 3x-6 find (f*g)(x) and (f/g)(x).
What is (f*g)(x)=3x^3 -12x^2 +12x and (f/g)(x)= x/3
200
Solve cube root of (4x+8) +3= 7 and check answer.
What is 14.
200
The number of turning points a polynomial will have is the same number as the..
What is degree-1/ highest power-1/ greatest exponent-1
300
The inverse of f(x)=-16+x^3
What is f^-1(x)= cube root of x+16
300
State the transformation for the function f(x)= |x-2|-1
shifts right 2, down 1
300
Find (fog)(x), (gof)(x), (fog)(3). f(x)= x^2 +1 g(x)= x-4
What is (fog)(x)= x^2 -8x+17 (gof)(x)= x^2 -3 (fog)(3)=5
300
Solve 2x=square root of (28x+29) -3
What is -1 and 5.
300
The coefficient before the variable with the highest exponent is called the…
What is leading coefficient
400
Prove that f(x)=x^2 +10 and g(x)=square root of x-10 are inverses of each other.
What is f(g(x))=x and g(f(x))=x; therefore they are inverses of one another.
400
State the transformation of the function f(x)= - square root of (x+4)
shifts left 4 and reflected on x-axis
400
Find (fog)(x), (gof)(x), (fog)(3). f(x)= 6x^2 -4 g(x)= x+2
What is (fog)(x)= 6x^2 +24x+20 (gof)(x)= 6x^2 -2 (fog)(3)= 146
400
Solve 12= cube root of (x-2)^2 +8
What is 10 and -6.
400
State the number of possible real zeros, turning points, and leading coefficient of the function and determine all of the real zeros by factoring. f(x)=3x^5 -18x^4 +27x^3
What is 5 real zeros, 4 turning points, leading coefficient= 3. Zeros = 0 and 3
500
Prove that f(x)= (x+4)/x and g(x)=4/(x-1) are inverses of one another.
What is f(g(x))= x and g(f(x))= x; therefore f(x) and g(x) are inverses of each other.
500
Write the equation for the graph on the board.
What is f(x)=|x+4|-8
500
Find (fog)(x) f(x)= square root of (x-1) g(x)= (x-1)^2
What is (fog)(x)= square root of (x^2 -2x)
500
Solve. 7+ cube root of (1054-3x)=11
What is 10.
500
State the number of possible real zeros, turning points, and leading coefficient of the function and determine all of the real zeros by factoring. f(x)=x^4 -4x^3 -32x^2
What is 4 possible zeros, 3 turning points, leading coefficient= 1 and zeros= 0,8, and -4