Pre-Calculus Semester Exam Review

Front

What is the center and radius of the circle with the equation (x-4)²+(y+2)²=25?

Back

C:(4, -2), r=5

Front

What is the value of √-36?

Back

6i

Front

How do you find the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be found by comparing the degrees of the numerator and denominator.

Front

What is the increasing interval of the function f(x) = x² - 4x?

Back

(-∞, 1) U (3, ∞)

Front

What is the decreasing interval of the function f(x) = -x² + 4x?

Back

(1, 3)

Front

What is the standard form of a circle's equation?

Back

(x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

Front

What is the definition of a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.

Front

How do you determine the center and radius from the equation of a circle?

Back

Identify h and k from (x-h)² + (y-k)² = r²; the center is (h,k) and r is the radius.

Front

What is the formula for finding the vertex of a parabola in standard form?

Back

The vertex (h,k) can be found using h = -b/(2a) for the quadratic equation ax² + bx + c.

Front

What is the relationship between the degrees of the numerator and denominator in rational functions?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0.