Theory question 106
Graphs of Functions(a) Draw the table of values for the relation y = x2 for the interval −3 ≤ x ≤ 4. (b) Using a scale of 2 cm to 1 unit on the x-axis and 2cm to 2 units on the y-axis, draw the graphs of: (i) y = x2 (ii) y = 2x + 3 for −3 ≤ x ≤ 4. (c) Use your graph to find: (i) the roots of the equation x2 = 2x + 3; (ii) the gradient of y = x2 at x = −2.
Show the model answer
Model answer
(a) x: −3, −2, −1, 0, 1, 2, 3, 4; y: 9, 4, 1, 0, 1, 4, 9, 16.
(b) Plot the parabola and the straight line through (0, 3) and (3, 9).
(c)(i) The graphs meet at x = −1 and x = 3.
(ii) Draw the tangent at (−2, 4); its gradient is about −4.
Explanation
To find a gradient from a graph, draw a tangent and use rise ÷ run.