Function Composition Flashcard

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition of f and g is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find p(p(-3)) if p(x) = 3x + 4?

Back

First, find p(-3): p(-3) = 3(-3) + 4 = -9. Then, find p(-9): p(-9) = 3(-9) + 4 = -27 + 4 = -23.

Front

What is the value of f(4) if f(x) = x² - 5x?

Back

f(4) = 4² - 5(4) = 16 - 20 = -4.

Front

How do you evaluate f(g(0)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

First, find g(0): g(0) = 0 - 2 = -2. Then, find f(-2): f(-2) = 3(-2) + 10 = -6 + 10 = 4.

Front

What is f(10) if f(x) = -2x + 13?

Back

f(10) = -2(10) + 13 = -20 + 13 = -7.

Front

What does it mean if f(x) = 16 has two solutions?

Back

It means that the function intersects the line y = 16 at two points, indicating that there are two x-values that satisfy the equation.

Front

How do you find the roots of the equation f(x) = 0?

Back

Set the function equal to zero and solve for x. For example, if f(x) = x² - 4, set x² - 4 = 0, which gives x = ±2.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, indicating the maximum or minimum value.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its derivative is positive over an interval and decreasing if its derivative is negative.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax² + bx + c, where a ≠ 0.