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How to Find Inverse Functions: Video Lesson How to Find an Inverse Function To find an inverse function: Replace the ‘f(x)=’ in the equation with ‘y=’. Replace every x in the equation with a y and the y with an x. Solve this equation for y. Replace the y with an f-1(x). For example, find […]

How to Find the Angle Between Two Vectors: Video Lesson Angle Between Two Vectors Calculator The calculator below calculates the angle between 2D and 3D vectors. Simply enter the components of each vector in the form How to Find the Angle Between Two Vectors To find the angle between two vectors: Find the dot product

Completing the Square Video Lesson How to Complete the Square To complete the square for 𝑥2+b𝑥+c: Divide b by 2 and write this inside brackets squared as (𝑥 + b/2)2 Square the value of b/2 and subtract it. Add the constant term of c to this result. The final result is given by (𝑥 +

Finding Stationary Points: Video Lesson What are Stationary Points? Stationary points are the points on a function where its derivative is equal to zero. At these points, the tangent to the curve is horizontal. Stationary points are named this because the function is neither increasing or decreasing at these points. There are 3 types of

How to Find and Graph x and y Axis Intercepts Video Lesson How to Find x and y axis intercepts To find an x intercept, substitute y = 0 into the equation and solve for x. To find the y axis intercept, substitute x = 0 into the equation and solve for y. For example,

Sign Diagram Video Lessons How to Make a Sign Diagram for a Function How to Make a Sign Diagram from a Graph What is a Sign Diagram? A sign diagram shows the intervals where a function has positive or negative outputs. The 𝑥-axis intercepts are written on the axis of the sign diagram. In between

Composite Functions Video Lesson How to Find Composite Functions To find a composite function: Identify the outer and inner functions. Write the outer function. Substitute each 𝑥 with the inner function. Simplify if necessary. For example, if and , calculate . 1. Identify the outer and inner functions For the composite function , the is

The Discriminant Video Lesson What is the Discriminant of a Quadratic Equation? The discriminant is the part of the quadratic formula found within the square root. For a quadratic of the form a𝑥2 + b𝑥 + c, its discriminant is b2 – 4ac. A quadratic equation has 2, 1 or 0 solutions depending if the

Probability Tree Video Lessons Independent Probability Trees: Video Lesson Conditional Probability Trees: Video Lesson How to Draw a Probability Tree To make a probability tree: Draw a branch for each outcome of the first event. Write the outcome at the end of each branch. Write the probability of each outcome next to the corresponding branch.

How to Use the Chain Rule Video Lesson The Chain Rule with Trigonometric Functions What is the Chain Rule? The chain rule is used to calculate the derivative of a composite function. The chain rule formula states that dy/dx = dy/du × du/dx. In words, differentiate the outer function while keeping the inner function the