Precalculus Flashcard 9 (Fall Semester Review)

Front

What is the composition of functions?

Back

The composition of functions, denoted as (g ∘ f)(x), means applying function f first and then applying function g to the result. It is defined as g(f(x)).

Front

How do you find the composition of f(x) = x^2 - 1 and g(x) = 4x - 3?

Back

To find (g ∘ f)(x), substitute f(x) into g: g(f(x)) = g(x^2 - 1) = 4(x^2 - 1) - 3 = 4x^2 - 4 - 3 = 4x^2 - 7.

Front

What does it mean to solve an inequality?

Back

Solving an inequality involves finding the values of the variable that make the inequality true, often resulting in a range of values.

Front

How do you solve the inequality (x - 1)(x - 2)(x - 4) ≤ 0?

Back

Find the critical points (1, 2, 4), test intervals, and determine where the product is less than or equal to zero. The solution is (-∞, 1] ∪ [2, 4].

Front

What is a square root equation?

Back

Front

Back

Square both sides to eliminate the square roots: 9x - 2 = 3x + 10. Solve for x: 6x = 12, so x = 2.

Front

What is function evaluation?

Back

Function evaluation is the process of finding the output of a function for a specific input value.

Front

How do you evaluate g(1 + 5m) for g(x) = 2x^2 + 18x - 14?

Back

Substitute 1 + 5m into g: g(1 + 5m) = 2(1 + 5m)^2 + 18(1 + 5m) - 14 = 50m^2 + 110m + 6.

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, while a relation can have multiple outputs for a single input.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.