Unit 3 College Algebra Practice

Front

What is function composition and how is it denoted?

Back

Function composition is the process of applying one function to the results of another function. It is denoted as (g ∘ f)(x) = g(f(x)).

Front

Evaluate (g ∘ f)(4) if f(x) = 6x - 2 and g(x) = 2x^2 + 4.

Back

To evaluate (g ∘ f)(4), first find f(4) = 6(4) - 2 = 22, then g(22) = 2(22)^2 + 4 = 968. The answer is 968.

Front

What is the difference between two functions k(x) and f(x)?

Back

The difference of two functions k(x) and f(x) is defined as (k - f)(x) = k(x) - f(x).

Front

Given f(x) = 6x - 2 and k(x) = x^2 - 3x, find (k - f)(x).

Back

(k - f)(x) = (x^2 - 3x) - (6x - 2) = x^2 - 9x + 2.

Front

What is the significance of the number 4 in relation to its spelling?

Back

The number 4 is unique because it has the same number of letters in its name ('four') as its value.

Front

How do you determine the intervals where a function is increasing?

Back

To determine where a function is increasing, find the derivative of the function and identify where it is positive.

Front

Identify the intervals where the function is increasing if the intervals are (-3,-2) U (-1,1) U (2,4].

Back

The function is increasing in the intervals (-3,-2), (-1,1), and (2,4].

Front

Evaluate h(9) + f(2) if h(x) = 3 - 2x and f(x) = 6x - 2.

Back

h(9) = 3 - 2(9) = -15 and f(2) = 6(2) - 2 = 10. Therefore, h(9) + f(2) = -15 + 10 = -5.

Front

What is the formula for the composition of two functions f and g?

Back

The formula for the composition of two functions f and g is (g ∘ f)(x) = g(f(x)).

Front

What does it mean for a function to be defined piecewise?

Back

A piecewise function is defined by different expressions based on the input value, often using intervals.