2024 1st Semester Exam

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 f(g(x)) means to apply g first and then apply f to the result.

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is f(g(0))?

Back

f(g(0)) = f(-2) = 3(-2) + 10 = 4.

Front

What is the result of f(g(x)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

f(g(x)) = f(x - 2) = 3(x - 2) + 10 = 3x - 6 + 10 = 3x + 4.

Front

If f(x) = x - 5 and g(x) = 3x^2 - 1, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.

Front

Given f(x) = 2x and g(x) = x^2 + 3, find f(g(x)).

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

When f(x) = x^2 + 9 and g(x) = x - 9, find f(x) - g(x).

Back

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.