Chapter 2 review

Front

What are x-intercepts?

Back

X-intercepts are the points where a graph crosses the x-axis, meaning the output (y-value) is zero. For example, in the point (-2,0), -2 is the x-intercept.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. The solutions are the x-values where the graph intersects the x-axis.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at that point.

Front

What is a hole in a graph?

Back

A hole occurs in a graph at a point where a function is not defined due to a factor that cancels out in the function's expression. It represents a removable discontinuity.

Front

How do you determine 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. Exclude values that make the denominator zero.

Front

What is the significance of the factor in a polynomial?

Back

A factor of a polynomial indicates a root or zero of the polynomial. If x = a is a root, then (x - a) is a factor.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where it does not produce a valid output, such as division by zero or taking the square root of a negative number.

Front

How do you find the zeros of the polynomial given one factor?

Back

If you know one factor of a polynomial, you can use polynomial division to divide the polynomial by that factor to find the remaining factors and their corresponding zeros.

Front

What is the relationship between zeros and x-intercepts?

Back

Zeros of a function are the x-values that make the function equal to zero, which correspond to the x-intercepts of the graph.

Front

What is the process for finding vertical asymptotes?

Back

To find vertical asymptotes, identify values of x that make the denominator of a rational function equal to zero, provided those values do not cancel with the numerator.