Function Notation and Image/Pre-image

This tutorial for Year 12 math students covers function notation, image, and pre-image concepts. It begins with an introduction to function notation, followed by examples of calculating function values and determining inputs for given outputs. The video also explains image and pre-image concepts, demonstrating how to find pre-images for specific outputs. The session concludes with a summary and an invitation for further questions.

What is the main focus of this tutorial?

• Calculus and derivatives

• Function notation and image/pre-image

• Statistics and probability

• Trigonometry and angles

What is the function notation used for?

• To calculate the area under a curve

• To express the relationship between input and output

• To denote the integral of a function

• To represent a function's derivative

What is the main topic of Exercise 1B mentioned in the tutorial?

• Function notation and image/pre-image

• Statistics

• Calculus

• Trigonometry

What is the function given in the tutorial?

• f(x) = x^2 - x + 1

• f(x) = x^3 + x - 1

• f(x) = x^2 - x - 1

• f(x) = x^2 + x + 1

What is the value of f(x) when x = -2 for the function f(x) = x^2 - x + 1?

• 8

• 7

• 6

• 5

What is the result of f(-2) for the function f(x) = x^2 - x + 1?

• 8

• 5

• 6

• 7

If f(a) = 13 for the function f(x) = x^2 - x + 1, what are the possible values of a?

• 4 and -3

• 5 and -2

• 2 and -3

• 3 and -4

What type of function is f(x) = x^2 - x + 1?

• Quadratic

• Exponential

• Cubic

• Linear

What is the value of a if f(a) = 13 for the function f(x) = x^2 - x + 1?

• 2 and -3

• 3 and -4

• 5 and -2

• 4 and -3

What is the image of 3 for the function f(x) = √(x + 1)?

• 2

• 1

• 3

• 4