NC Math 4 Review for Final Exams

Front

What is the composition of functions?

Back

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

Front

How do you find f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

First, calculate g(5): g(5) = 5 - 2 = 3. Then, find f(3): f(3) = 3(3) + 10 = 19.

Front

What are domain restrictions in a function?

Back

Domain restrictions are the values of x for which a function is defined. They indicate the input values that are valid for the function.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the lowest and highest y-values that the graph reaches.

Front

What does the notation y = log_b(x) represent?

Back

The notation y = log_b(x) represents the logarithm of x to the base b, which answers the question: 'To what power must b be raised to obtain x?'

Front

What is the significance of the base in a logarithmic function?

Back

The base of a logarithmic function determines the rate of growth of the function. Different bases will produce different graphs.

Front

How do you match a graph with its equation?

Back

To match a graph with its equation, analyze key features such as intercepts, asymptotes, and overall shape to find the corresponding equation.

Front

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

Back

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

Front

What is the difference between domain and range?

Back

Domain refers to the set of possible input values (x-values) for a function, while range refers to the set of possible output values (y-values).