PDF Notes: Unit 1 - Notes - Precalc and Limits

How do you calculate the slope of a line through points A(-2, 5) and B(4, -7)?

Use the formula m = (y2 - y1) / (x2 - x1).

What is the relationship between the slopes of parallel lines?

They have equal slopes.

What condition defines perpendicular lines in terms of their slopes?

The product of their slopes equals -1.

What is the slope of a horizontal line?

It is 0.

What is the slope of a vertical line?

It is undefined.

What is the slope-intercept form of a linear equation?

y = mx + b.

What does the vertical line test determine?

If a curve represents a function.

How is an even function defined?

f(-x) = f(x) for all x in the domain.

What characterizes an odd function?

f(-x) = -f(x) for all x in the domain.

What does interval notation represent?

A way to describe a range of values.

What is the definition of exponential growth?

Occurs when a > 1 in the function y = k * a^k.

What indicates exponential decay in a function?

0 < a < 1 in the function y = k * a^k.

What is the formula for continuous compound interest?

y = P * e^(rt).

What does the number e represent in exponential functions?

The base of natural logarithms, approximately 2.718.

What is the initial value in the exponential growth model B = 100 * e^(0.693t)?

100 bacteria.

How do you find the rate of growth from a population increase?

Use the formula for exponential growth to solve for r.