Summary
◦ Given a function, you put an x value in and get an f(x) or y value out.
◦ Look for ways to use Plugging In and PITA on function questions.
◦ For questions about the graphs of functions, remember that f(x) = y.
◦ If the graph contains a labeled point or the question gives you a point, plug it into the equations in
the answers and eliminate any that aren’t true.
◦ The equation of a line can take two forms. In either form, (x, y) is a point on the line.
- In slope-intercept form, y = mx + b, the slope is m, and the y-intercept is b.
- In standard form, Ax + By = C, the slope is - , and the y-intercept is .
◦ Given two points on a line, (x 1 , y 1 ) and (x 2 , y 2 ), the slope is .
◦ Two linear equations with infinitely many solutions actually represent the same line.
◦ Parallel lines have the same slopes and no points of intersection.
◦ Perpendicular lines have slopes that are negative reciprocals and intersect at a right angle.
◦ To find a point of intersection, plug the point into both equations to see if it works or graph the lines
on your calculator when it is allowed.
◦ To find the midpoint between two points, average the x-coordinates and average the y-coordinates.
◦ To find the distance between two points, make them the endpoints of the hypotenuse of a right
triangle and use Pythagorean Theorem.
◦ The roots of a function, also known as solutions, zeroes, or x-intercepts, are the points where the
graph crosses the x-axis and where y = 0.
◦ Graphs of functions can be moved up or down if a number is added to or subtracted from the
function, respectively. They can move left if a number is added inside the parentheses of the function
or move right if a number is subtracted inside the parentheses.
◦ The vertex form of a parabola equation is y = a(x − h)^2 + k, where (h, k) is the vertex. To get a
parabola in the standard form into vertex form, complete the square.
◦ The standard form of a circle equation is (x − h)^2 + (y – k)^2 = r^2 , where (h, k) is the center and r is
