Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find the product of two binomials, such as (a + b)(c + d)?

Back

Use the distributive property (FOIL method): Multiply the first terms, outer terms, inner terms, and last terms, then combine like terms.

Tags

CCSS.HSA.APR.A.1

Front

What is the result of (y - 3)(y + 7)?

Back

y² + 4y - 21.

Tags

CCSS.HSA.APR.A.1

Front

What is the result of (x + 2)(x + 3)?

Back

x² + 5x + 6.

Tags

CCSS.HSA.APR.A.1

Front

How do you evaluate a function at a specific point, such as f[g(5)]?

Back

First, find g(5), then substitute that result into f.

Tags

CCSS.HSF-BF.A.1C

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is g(h(x))?

Back

g(h(x)) = 9x + 1.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for simplifying (x - a)²?

Back

(x - a)² = x² - 2ax + a².

Tags

CCSS.HSA.APR.C.4

Front

What is the result of simplifying (x - 7)²?

Back

x² - 14x + 49.

Tags

CCSS.HSA.APR.C.4

Front

What does it mean to combine like terms in algebra?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Tags

CCSS.7.EE.A.1

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output.

Tags

CCSS.8.F.A.1