Functions and Their Properties

This video tutorial covers essential pre-calculus topics, focusing on functions, their graphs, domains, and ranges. It explores various parent functions, including linear, quadratic, cubic, and more, and explains how to determine their domains and ranges. The tutorial also delves into transformations and reflections of functions, composition of functions, and finding inverse functions. Each concept is illustrated with examples to enhance understanding.

What is the domain of a quadratic function?

• Numbers greater than zero

• Only negative numbers

• Only positive numbers

• All real numbers

What is the range of the function y = |x|?

• All real numbers

• Negative infinity to zero

• Negative infinity to infinity

• Zero to infinity

For the function y = 1/x, what value must be excluded from the domain?

• -1

• 0

• 1

• Infinity

What is the range of the exponential function e^x?

• All real numbers

• Negative infinity to infinity

• Zero to infinity

• Negative infinity to zero

What is the domain of the natural log function ln(x)?

• x = 0

• x < 0

• x > 0

• All real numbers

Which trigonometric function has a range from -1 to 1?

• Secant

• Tangent

• Sine

• Cosecant

How does the graph of y = sin(x) differ from y = -sin(x)?

• It shifts up

• It shifts down

• It reflects over the x-axis

• It reflects over the y-axis

What effect does a negative sign outside a function have on its graph?

• Reflects over the x-axis

• Reflects over the y-axis

• Shifts the graph down

• Shifts the graph up

What is the effect of adding a constant inside the function f(x - c)?

• Shifts the graph up

• Shifts the graph down

• Shifts the graph left

• Shifts the graph right

What is the inverse of the function f(x) = x^2 with a restricted domain x ≥ 0?

• f(x) = 1/x

• f(x) = x^2

• f(x) = √x

• f(x) = -x