iGCSE Mathematics (0580) :E2.11Draw and interpret graphs representing exponential growth and decay problems.iGCSE Style Questions Paper 2

Question

On the axes, sketch the graph of each of these functions:

(a) $y=\frac{1}{x}$

(b) $y=4^{x}$

▶️ Answer/Explanation

Answer:

(a) Hyperbola with two branches in quadrants I & III, approaching but never touching the axes.

(b) Exponential curve increasing rapidly for $x > 0$, approaching 0 for $x < 0$, passing through (0,1).

Question

The graph of a cubic function has two turning points.
When $x < 0$ and when $x > 4$ the gradient of the graph is positive.
When $0 < x < 4$ the gradient of the graph is negative.
The graph passes through the origin.

Sketch the graph.

▶️ Answer/Explanation

Solution

Sketch should show:

1. A cubic curve with maximum at origin (0,0)

2. A minimum point somewhere in the range 0 < x < 4

3. Positive gradient for x < 0 and x > 4

4. Negative gradient between 0 < x < 4

iGCSE Mathematics (0580) :E2.11Draw and interpret graphs representing exponential growth and decay problems.iGCSE Style Questions Paper 2

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