Functions and Graphing on the GED Math Test

Marks go missing because the wrong answers look right. If the slope is 2/3, then 3/2 and −2/3 are also among the choices, and a plan costing $25 to start plus $10 a month is offered as y = 25x + 10 beside the correct y = 10x + 25. The set below targets those slips.

This topic is a whole reporting category by itself: GED Testing Service calls it “algebraic problem solving with graphs and functions”, indicators A.5.a through A.7.d, and weights it at about 25% of the test. On about 46 questions that is roughly eleven or twelve items, by our arithmetic rather than any official count.

Skills in this set: Slope from two points · Plotting points on the coordinate plane · Slope from a graph · Slope from a table of values · Writing a linear equation from a description · Finding intercepts from an equation · Matching a graph to its equation · Identifying a point on a line · Plotting a point from an equation · Evaluating functions in function notation · Reading function values from a table · Comparing linear functions in different forms · Recognizing a function from a table · Unit rate as the slope of a proportional relationship · Interpreting slope and intercept in context · Solving a system of equations by graphing · Deciding whether a table is linear · Writing the equation of a line through two points

What the test asks

The Assessment Guide for Educators lists A.5.a through A.7.d. In plain terms: plotting points (A.5.a); slope from a graph, equation or table, including a unit rate as a slope (A.5.b, A.5.c); graphing a line and reading its intercepts (A.5.d, A.5.e); the equation of a line from a slope and a point or from two points (A.6.a, A.6.b); parallel and perpendicular slopes (A.6.c); comparing two rates in different forms (A.7.a); whether a table is a function (A.7.b); evaluating f(x) (A.7.c); and comparing an equation with a table (A.7.d). Solving a system where two lines cross sits under A.2.d, but it is graph reading, so the set includes it.

Money over time is the usual story: a gym with a sign-up fee plus a monthly charge, a phone plan with an activation fee, savings that grow by $15 a week. The slope m is the amount that repeats; b is the amount paid once or already there. Function notation is the part many GED courses skip: A.7.c has you evaluate a rule written as f(x), where f(3) means put 3 wherever x appears.

Nothing in the official record says which topics fill the roughly five no-calculator questions that open the test, but a slope counted off a grid or f(−2) needs only small whole numbers, so expect that they can. Some items are hot spots, where you click the grid to plot a point.

The mistakes this set is built to catch

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

A worked example

How to practice it

1. Count the rise and run between two lattice points you can read exactly, where the line crosses a grid corner. Put a finger on the left one, count squares up or down to the level of the right one, then across, and put the rise on top.
2. With the slope formula, write the two points one above the other and subtract the lower point from the upper one in both the numerator and the denominator, even when the numbers are easy. The order, rather than the arithmetic, is what produces sign errors.
3. Read f(3) out loud as “the output when the input is 3”, and put brackets around the input before you substitute, so f(x) = 2x² − 5 at −3 becomes 2(−3)² − 5. Then square, multiply, and add or subtract, in that order.
4. Before comparing two functions, get both into the same form: divide the table’s change in y by its change in x, write that rate beside the m from the equation, and only then compare. The starting values are a distraction planted on purpose.