PreCalc Exam Review - Semester 1

Front

What is the minimum point of a quadratic function?

Back

The minimum point of a quadratic function is the vertex of the parabola when it opens upwards. For example, in the function f(x) = ax^2 + bx + c (where a > 0), the vertex can be found at x = -b/(2a).

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts of a function, set the function equal to zero and solve for x. The solutions are the points where the graph crosses the x-axis.

Front

What are discontinuities in a function?

Back

Discontinuities are points at which a function is not continuous. They can be classified as removable (holes) or non-removable (asymptotes).

Front

What determines the horizontal asymptote of a rational function?

Back

The horizontal asymptote of a rational function is determined by the degrees of the numerator and denominator. If the degree of the numerator is less than that of the denominator, the horizontal asymptote is y = 0.

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (y-value) decreases as x increases. It can be identified by analyzing the function's derivative.

Front

How do you identify holes in a rational function?

Back

Holes occur in a rational function when a factor in the numerator and denominator cancels out. The x-value of the hole is the value that makes the canceled factor equal to zero.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola, indicating the highest or lowest value of the function.

Front

How do you determine the intervals of increase and decrease for a function?

Back

To determine intervals of increase and decrease, find the derivative of the function. Analyze where the derivative is positive (increasing) or negative (decreasing).

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial determines its end behavior. For even degrees, the ends go in the same direction; for odd degrees, they go in opposite directions.

Front

What is the difference between a hole and an asymptote?

Back

A hole is a point where the function is undefined due to a canceled factor, while an asymptote is a line that the graph approaches but never touches.