IM2H Midterm Review

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(g(x)) for f(x) = 9 - 3x and g(x) = 5x - 7?

Back

To find f(g(x)), substitute g(x) into f(x): f(g(x)) = 9 - 3(5x - 7) = 9 - 15x + 21 = 30 - 15x.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

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

Back

To determine intervals of increase or decrease, analyze the derivative of the function. If f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What is the significance of the point (0, 6) in a function's graph?

Back

The point (0, 6) represents a specific value of the function at x = 0. Depending on the context, it could be a maximum, minimum, or neither.

Front

What is a relative minimum?

Back

A relative minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points.

Front

What is an absolute maximum?

Back

An absolute maximum is the highest point over the entire domain of a function, meaning no other point has a greater function value.

Front

How do you identify decreasing intervals of a function?

Back

Decreasing intervals can be identified by finding where the derivative of the function is negative (f'(x) < 0).

Front

What does the notation (-∞, 2) U (-2, ∞) represent?

Back

This notation represents the union of two intervals: all real numbers less than 2 and all real numbers greater than -2.

Front

What is the value of f(-3) if f(x) is defined by a graph?

Back

To find f(-3), locate the point on the graph where x = -3 and read the corresponding y-value.