Spiral Review 8 (March 17 - 21)

Front

What is the domain of the inverse function \( g^{-1}(x) \) if the range of \( g(x) \) is \([3, \infty)\)?

Back

The domain of \( g^{-1}(x) \) is \([3, \infty)\).

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs produce the same output.

Front

Identify a one-to-one function from the following: \( y=7|x| \), \( y=7x^2 \), \( y=7\sqrt{x} \), \( y=7 \).

Back

The one-to-one function is \( y=7\sqrt{x} \).

Front

What is the range of a function if its domain is \( (-\infty, \infty) \)?

Back

The range can also be \( (-\infty, \infty) \) depending on the function.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, for any two points \( x_1 \) and \( x_2 \) in its domain, if \( x_1 < x_2 \), then \( f(x_1) < f(x_2) \).

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If any vertical line intersects the curve more than once, it is not a function.

Front

What is the significance of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine if a function is one-to-one using its graph?

Back

A function is one-to-one if any horizontal line intersects the graph at most once.

Front

What is the inverse of a function?

Back

The inverse of a function \( f \) is a function \( f^{-1} \) that reverses the effect of \( f \), such that \( f(f^{-1}(x)) = x \) for all x in the range of \( f \).