01/10 Functions and Modeling Free Online FlashCards

What is a function?

A function assigns exactly one output to each input.

What does f(x) mean?

Function notation gives the output for an input; f(x) means “f of x,” not f multiplied by x.

How do domain and range differ?

The domain is the set of allowable inputs, while the range is the set of resulting outputs.

What is the domain restriction for (x+2)/(x−3)?

For f(x)=(x+2)/(x−3), exclude x=3 because a denominator cannot equal zero.

Which four representations commonly describe a function?

A table, graph, formula, and verbal rule are equivalent representations when they describe the same input-output relationship.

How does the vertical line test identify a function?

The vertical line test: a graph represents a function if every vertical line intersects it at most once.

What do 3 and 2 represent in f(x)=3x+2?

In f(x)=3x+2, the coefficient 3 is the rate of change and 2 is the initial value f(0).

Describe the transformation from x² to (x−4)²+2.

The graph of g(x)=(x−4)^2+2 is shifted right 4 units and up 2 units from y=x^2.

Which function is evaluated first in (f∘g)(x)?

Composition applies the inner function first: (f∘g)(x)=f(g(x)).

When does a function have an inverse function?

A function has an inverse only when it is one-to-one on the specified domain; the horizontal line test checks this graphically.

What is the inverse of f(x)=3x−5?

For f(x)=3x−5, interchange x and y and solve to obtain f⁻¹(x)=(x+5)/3.

What is the domain of g(x)=√(x−5)?

For g(x)=√(x−5), require x−5≥0, so the domain is [5,∞).