Question

4.1.5) graph the function on the coordinate plane below. include three right triangles that connect four points on the graph line. one point must be the y-intercept. also, use arrowheads on both ends of the graph.

4.1.6) use the ordered pairs to create a mapping of the function.

Explanation:

Step1: Identify the Function (Assume a Linear Function)

Let's assume a linear function, say \( y = 2x + 3 \). The y - intercept is when \( x = 0 \), so \( y=3 \). So the point \( (0,3) \) is the y - intercept.

Step2: Find Other Points

• For \( x = 1 \), \( y=2(1)+3 = 5 \), so the point is \( (1,5) \).
• For \( x=- 1 \), \( y=2(-1)+3 = 1 \), so the point is \( (-1,1) \).
• For \( x = 2 \), \( y=2(2)+3 = 7 \), so the point is \( (2,7) \).

Step3: Graph the Points and Line

Plot the points \( (0,3) \), \( (1,5) \), \( (-1,1) \), \( (2,7) \) on the coordinate plane. Draw a straight line through them with arrowheads on both ends.

Step4: Create Right Triangles

• Between \( (0,3) \) and \( (1,5) \): Move 1 unit right (along x - axis) and 2 units up (along y - axis) to form a right triangle.
• Between \( (0,3) \) and \( (-1,1) \): Move 1 unit left (along x - axis) and 2 units down (along y - axis) to form a right triangle.
• Between \( (1,5) \) and \( (2,7) \): Move 1 unit right (along x - axis) and 2 units up (along y - axis) to form a right triangle.

Step5: Create Mapping (for 4.1.6)

The ordered pairs are \( (0,3) \), \( (1,5) \), \( (-1,1) \), \( (2,7) \). The mapping will have the set of x - values \( \{ - 1,0,1,2\} \) and the set of y - values \( \{1,3,5,7\} \), with arrows from each x to its corresponding y.

Answer:

(For graphing: The line passes through (0,3), (1,5), (-1,1), (2,7) with arrowheads. Right triangles as described. For mapping: x - values {-1,0,1,2} mapped to y - values {1,3,5,7} respectively)