MHF4UV

Unit 1

100

How can you test for a function 

Vertical line test 

200

What is the Quadratic formula 

(-b±√(b²-4ac))/(2a)

300

Answer the following 

(x−5)(2x+3)=0

x=5 x=−3/2

400

Given the polynomial f(x)=3x³−4x²+5x−, use the Remainder Theorem to find the remainder when f(x) is divided by x−2.

16

500

Solve the following quadratic equation for x: 2x²−4x−6=0

The roots of the equation 2x²−4x−6=0 are x=3 and x=−1.

Unit 2

100

What is the mapping rule?

(x,y)= x/k+d, ay+c

200

What is a RATIONAL functions 

A rational function is a ratio of two polynomials

300

What does the a value affect in a function 

The a value in a function typically affects the vertical stretch/compression and the direction of the graph.

400

What makes a function ODD

If f(-x)= -f(x), symmetric about the origin 

500

What makes a function even?

if f(-x) = f(x), symmetric about the y-axis 

Unit 3

100

What is a logarithmic function? 

A logarithmic function is the inverse of an exponential function. 

200

when there is no base on a log, what is assumed to be the number?

10

300

How many power laws of logs are there?

3

400

what are the 3 log power laws?

• Product Rule: log⁡_b(xy)=log⁡_b(x)+log⁡_b(y)
• Quotient Rule: log⁡_b(xy)=log⁡_b(x)−log⁡_b(y)
• Power Rule: log⁡_b(xk)=k⋅log⁡_b(x)

500

How do you graph a logarithmic function?

1. Identify Key Points: Start with x=1 (where log⁡b(1)=0 and x=b(where log⁡b(b)=1.
2. Plot the Asymptote: Draw a vertical dashed line at x=0x=0 (the y-axis is a vertical asymptote).
3. Sketch the Curve: The graph increases slowly, passing through the key points and approaching the vertical asymptote as xapproaches 0 from the right.

Unit 4

100

How many special triangles are there 

2

200

How do you convert Degrees into Rads 

Pi/180

300

How do you convert rads into degrees 

Degree= Rad(180/pi)

400

What does the CAST rule tell us 

when a function falls into its respective quadrant it is positive. C(cos and sec) A (all) S(sin and csc) T ( tan and cot)

500

What is the amplitude formula 

Max-Min

  2

Unit 5

100

How can we tell a rational function? 

 There are two vertical asymptotes and one horizontal asymptote. 

NOTE: no other functions studied in this course have both asy's.

200

What is a compound function 

A compound function, also known as a composite function, is a function that is created by combining two functions. If you have two functions f and g, the composite function f∘g looks like this.   

(f∘g)(x)=f(g(x))

300

What is Average Rate of Change 

A comparison of the change in the dependent variable with the change in the independent variable between two points on an interval of the function's domain

400

What is instantaneous rate of change ?

• A comparison of the change in the dependent variable with the change in independent variable at a single point on the function's domain.

500

Consider the function f(x)=3x+2. Find the average rate of change of the function over the interval [1,4].

3.