Junior Cycle Mathematics Functions: Draw each of the following two f

Draw each of the following two functions in the domain −2 ≤ x ≤ 2, for x ∈ R - Junior Cycle Mathematics - Question 10 - 2019

Question 10

Draw each of the following two functions in the domain −2 ≤ x ≤ 2, for x ∈ R. Show your working out. Function: y = 10x − 4x² Function: y = 3^x

Worked Solution & Example Answer:Draw each of the following two functions in the domain −2 ≤ x ≤ 2, for x ∈ R - Junior Cycle Mathematics - Question 10 - 2019

Step 1

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Answer

To graph the function y = 10x − 4x², we need to calculate the values of y for specific values of x in the domain −2 ≤ x ≤ 2.

**Calculate Key Points: **
- For x = -2: y = 10(-2) − 4(-2)² = -20 − 16 = -36.
- For x = -1: y = 10(-1) − 4(-1)² = -10 − 4 = -14.
- For x = 0: y = 10(0) − 4(0)² = 0.
- For x = 1: y = 10(1) − 4(1)² = 10 − 4 = 6.
- For x = 2: y = 10(2) − 4(2)² = 20 − 16 = 4.
Plotting Points:
- Plot the points (-2, -36), (-1, -14), (0, 0), (1, 6), and (2, 4).
Drawing the Graph:
- Join the points smoothly to show the parabolic curve. The parabola opens downward due to the negative coefficient of x².

Step 2

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Answer

To graph the function y = 3^x, calculate the values of y for key values of x in the domain −2 ≤ x ≤ 2.

Calculate Key Points:
- For x = -2: y = 3^(-2) = 1/9 ≈ 0.11.
- For x = -1: y = 3^(-1) = 1/3 ≈ 0.33.
- For x = 0: y = 3^(0) = 1.
- For x = 1: y = 3^(1) = 3.
- For x = 2: y = 3^(2) = 9.
Plotting Points:
- Plot the points (-2, 1/9), (-1, 1/3), (0, 1), (1, 3), and (2, 9).
Drawing the Graph:
- Join the points, creating a smooth curve that starts near the x-axis for negative x-values and rises steeply as x increases.