Connecting Function Representations

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Date:

📚 Part 1: Review, I can statements, and Multiple Choice (4 questions)

I can: translate between equations, tables, graphs, and verbal descriptions of functions.

Success criteria: identify matching representations, write an equation from a table or description, and explain reasoning clearly.

Differentiation: Extra scaffolding: show one example worked step-by-step. Challenge: create a non-linear example. Dyslexia-friendly: use high-contrast print, short sentences, and read-aloud option.

1. Which table matches the equation y = 2x + 1?

Table A: x=0→1, x=1→3, x=2→5

Table B: x=0→1, x=1→2, x=2→3

Table C: x=0→1, x=1→0, x=2→-1

Table D: x=0→2, x=1→4, x=2→6

2. Which verbal description matches the equation f(x) = -0.5x + 4?

The value decreases by 0.5 for each increase of 1 in x, starting at 4 when x = 0.

The value doubles each time x increases by 1, starting at 4.

The value increases by 0.5 for each increase of 1 in x, starting at 4.

The value stays constant at 4 for all x.

3. Which equation models a quantity that starts at 3 and doubles each hour?

y = 3 + 2x

y = 3(2^x)

y = 2(3^x)

y = 6x

4. Match each representation (left) to the best description (right). Draw lines between matching items.

A. Equation: y = 4x - 2

B. Table: x→0:5, 1:8, 2:11

C. Verbal: "Increases by 4 each time"

D. Graph: straight line through (0, -2) with slope 4

1. Shows starting value 5 at x=0

2. Linear function with slope 4 and y-intercept -2

3. Describes a constant increase of 4 per x

4. Equation y = 4x - 2

✏️ Part 2: Short Answers and Extensions (4 questions)

5. From this table: x→0:5, 1:9, 2:13. Write the linear equation f(x) = ____ . Show your work.

6. A line passes through (1, 2) and (3, 8). Find its equation in slope-intercept form. Show your steps.

7. Verbal to equation: "Temperature starts at 68°F and falls 3°F each hour." Write T(h) = ____.

8. Extension for advanced learners: A cube has side length s. Volume V = s^3 and surface area S = 6s^2. Express V as a function of S: V(S) = ____ . (Leave expression in simplest form.)

Extra supports: For students who need help, use a read-aloud and highlight one sentence at a time. For students ready to extend, create a non-linear matching set (quadratic or exponential) and explain differences.