Mississippi Math F-BF.3
The Standard
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Build New Functions from Existing Functions
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students change a function rule by adding or multiplying a number outside or inside the input. They predict how the graph moves, stretches, shrinks, or flips. They use a graphing tool to check their predictions and find the number used when given a graph.
What Mastery Looks Like
- A student can explain why f(x+2) moves left two units and why f(2x) is half as wide. They can identify which axis a negative multiplier reflects the graph across. Given an original and a changed graph, they can find the value used and check it with plotted points.
Common Misconceptions
- Students often move f(x+3) right instead of left, or think f(2x) makes a graph twice as wide. They may treat -f(x) and f(-x) as the same reflection.
How to Assess It
- Plot f(x)=x²+x+1 and four unlabeled graphs of f(x)-2, -2f(x), f(-2x), and f(x+2). On an exit ticket, ask students to name each change and give the value used.
Lesson moves
Ways to Teach It
Plot five points of f(x)=x²+x+1 on sticky notes; move them on graph paper to show f(x)+2 and f(x-2).
Ask pairs, 'Where does the point (0, f(0)) go on f(x+3), and why?'
Use Desmos sliders with f(x)=x²+x+1; partners test 2 and -2 in all four forms, then hide the values and guess from graphs.
Graph h(t)=-5t²+20t for a ball's height, then draw h(t-2) to show a launch delayed two seconds.
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