About this test · ~4 min read
What Practice Test 5 covers
Practice Test 5 is about functions and the coordinate plane. It emphasizes function notation, transformations of graphs, coordinate geometry, rate problems, and more demanding data analysis. This is the test where f(x) stops being a formula to evaluate and becomes an object you shift, stretch, and read off a graph.
Difficulty level
Medium-hard. Function transformations and coordinate reasoning push most students, even those who breezed through the computational tests.
Skills tested
- Function notation and evaluation
- Graph transformations: shifts, reflections, and stretches
- Distance, midpoint, and slope on the coordinate plane
- Unit rates and proportional reasoning
- Interpreting scatterplots and lines of best fit
Who should take this test
Students preparing for the harder half of the test bank who need fluency with function behavior. Take this once you can solve equations quickly and want to level up your graph reasoning.
Study tips
- Memorize the transformation rules: f(x) + k shifts up, f(x + k) shifts left, and −f(x) reflects over the x-axis.
- For rate problems, write the rate as a fraction with units and cancel the units to check your setup before computing.
- On scatterplots, describe the trend in words first — positive, negative, or none — before estimating a line of best fit.
Common mistakes
- Flipping the direction of a horizontal shift — f(x + 3) moves the graph left, not right.
- Confusing f(2), the output at x = 2, with the input value 2 itself.
- Reading a rate upside down (miles per hour vs. hours per mile) and inverting the answer.
Worked example
The function f(x) = a · 2^x passes through (0, 4) and (3, 32). What is a?
Use the first point. At x = 0, 2^0 = 1, so f(0) = a · 1 = a.
Since f(0) = 4, we get a = 4 directly.
Verify with the second point: f(3) = 4 · 2³ = 4 · 8 = 32, which matches (3, 32).
Both points are satisfied, so the value is confirmed.
Answer: a = 4.
Frequently asked questions
What is the hardest part of Practice Test 5?
For most students it is graph transformations. The horizontal shift rule feels backwards — f(x + k) moves left — so drill it until the direction is automatic.
How is function notation tested on the SAT?
You will evaluate f at specific inputs, read outputs off graphs, and interpret f(a) = b as a point on the curve. Test 5 mixes all three, so practice moving between the equation and the graph.
What should I know about lines of best fit?
You need to judge the direction and rough slope of the trend and use the line to predict values, not to compute a regression exactly. Focus on interpretation rather than calculation.
Are rate problems really function questions?
In spirit, yes — a constant rate is a linear function of time. Writing the rate with explicit units and treating it as slope keeps these problems from becoming guesswork.