24-25 Semester 1 Exam Part 2 (Makeup)

Front

What is the graph of the function y = sin(x)?

Back

The graph of y = sin(x) is a periodic wave that oscillates between -1 and 1, with a period of 2π.

Front

How do you find (h + g)(10) for h(x) = 3x + 3 and g(x) = -4x + 1?

Back

First, add h(x) and g(x): h(x) + g(x) = (3x + 3) + (-4x + 1) = -x + 4. Then plug in 10: (-10 + 4) = -6.

Front

What is the product of the functions f(x) = 4x + 8 and g(x) = x + 3?

Back

f(x) * g(x) = (4x + 8)(x + 3) = 4x^2 + 12x + 8x + 24 = 4x^2 + 20x + 24.

Front

What are points of discontinuity in a function?

Back

Points of discontinuity are values of x where a function is not continuous, meaning it is not defined or has a jump or infinite discontinuity.

Front

What is the graph of the function y = (1/x)?

Back

The graph of y = (1/x) is a hyperbola with two branches, one in the first quadrant and one in the third quadrant, approaching the axes but never touching them.

Front

Define a function.

Back

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

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.

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

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer.