18 (a) For each graph below, select its possible equation from this list - OCR - GCSE Maths - Question 18 - 2021 - Paper 1

The graph (ii) shows a steep decline approaching negative infinity and rising on the left side, suggesting an increasing function which aligns with the equation: $y = \sin x$. Thus, the answer is:

Answer

$y = \sin x$

To sketch $y = -x³$, reflect the graph of $y = x³$ across the x-axis. The graph will:

• Pass through the origin (0, 0).
• Decrease towards negative infinity as x approaches positive infinity.
• Increase towards positive infinity as x approaches negative infinity.

Sketch

A sketch would look similar to the following:

    | 
    |    |
    |   / 
   _|__|_____
    |   |\   
    |   | \  
    |   |_|  
    |__________
              

For the equation $y = x³ - 8$, we first recognize the y-intercept by setting x = 0:

$y = 0³ - 8 = -8$

This means the graph will pass through the point (0, -8). To find x-intercepts, set y = 0:

$x³ - 8 = 0$ $x³ = 8$ $x = 2$

Thus, the graph will cross the x-axis at (2, 0). The general shape will be the same as the base cubed function but translates downward 8 units.

Sketch

A sketch would represent:

    |  
    |    |
    |    |  
    |  . |           
 _0_|___|_____
    |    | 
    |    | 
    |    |__.
    |__________