Pre-cal Fall Semester Exam 24-25

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is the equation of the horizontal asymptote for the function f(x) = (2x^2 - 3)/(x^2 + 1)?

Back

y = 2

Front

What are the coordinates of a hole in a function?

Back

A hole occurs in a function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you find the coordinates of a hole in the function f(x) = (x + 1)(x - 2)/(x + 1)?

Back

The hole is at (-1, f(-1)) = (-1, ½) after simplifying the function.

Front

What is the multiplicity of a root?

Back

The multiplicity of a root refers to the number of times a particular root appears in a polynomial equation.

Front

What does it mean if a root has a multiplicity of 2?

Back

It means that the root is repeated twice, and the graph touches the x-axis at that point but does not cross it.

Front

What are the zeros of a function?

Back

The zeros of a function are the values of x for which f(x) = 0.

Front

How do you find the zeros of the function f(x) = (x + 3)(x + 1)(x - 2)(x - 5)?

Back

The zeros are x = -3, -1, 2, 5.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as x approaches a certain value, typically where the function is undefined.

Front

What is the equation of the vertical asymptote for the function f(x) = 1/(x - 4)?

Back

x = 4.