IB Math AI SL – Topic 2: Functions

Your formula sheet gives slope-intercept form as y = mx + c. Do you need to memorize this, or is it given?

It's given on the formula sheet — you just need to know how to use it

In y = mx + c, what does m represent?

The slope (gradient) of the line

In y = mx + c, what does c represent?

The y-intercept

Your formula sheet gives standard form as ax + by + d = 0. Is this something you need to memorize?

No, it's given — focus on being able to convert into and out of this form

Your formula sheet gives point-slope form as y - y1 = m(x - x1). What do m and (x1, y1) represent?

m is the slope, and (x1, y1) is a known point on the line

Your formula sheet gives the gradient formula as m = (y2-y1)/(x2-x1). What does this calculate?

The slope between two known points on a line

In IB math, what term is used interchangeably with "slope"?

Gradient

If two lines are parallel, what is true about their slopes?

They are equal

If two lines are perpendicular, what is true about their slopes?

They are negative reciprocals of each other, so m1 times m2 equals -1

What is a rational function?

A function that has a fraction with the variable in the denominator, e.g. f(x) = 1/x

What does the domain of a function mean?

All the possible x-values (inputs) the function can take

What does the range of a function mean?

All the possible y-values (outputs) the function can produce

What is interval notation used for?

Writing a domain or range as a continuous span between two endpoints instead of listing individual values

When reading domain and range off a graph, which direction do you read each one in?

Domain is read left to right along the x-axis, range is read bottom to top along the y-axis