iGCSE Mathematics (0580) : C2.10 Graphs of functions iGCSE Style Questions Paper 3

Question

(a) Complete the table of values for \(y=\frac{15}{x}.\)

(b) On the grid, draw the graph of \(y=\frac{15}{x}\) for \(-5\leq x\leq 5.\)

(d) Use your graph to solve \(\frac{15}{x}=6.\)

▶️ Answer/Explanation

Answer:

(a) −3, −5, −7.5, 7.5, 5, 3

(b) Hyperbola curve through plotted points

(d) x ≈ 2.5

Detailed Solution:

1. (a) Calculate each y-value by dividing 15 by the given x-values

2. (b) Plot all (x,y) points and connect them to form a hyperbola

3. (c) Draw a straight horizontal line crossing the y-axis at 6

4. (d) The solution is the x-coordinate where the hyperbola and y=6 line intersect

Question

(a) Complete the table of values for \( y = 4 + 3x – x^2 \)

\( x \)	-2	-1	0	1	2	3	4
\( y \)		0	4		6		0

(b) On the grid, draw the graph of \( y = 4 + 3x – x^2 \) for \( -2 \leq x \leq 4 \)

▶️ Answer/Explanation

Solution

(a) Answer: -6, 6, 4

For x = -2: \( y = 4 + 3(-2) – (-2)^2 = 4 – 6 – 4 = -6 \)

For x = 1: \( y = 4 + 3(1) – (1)^2 = 4 + 3 – 1 = 6 \)

For x = 3: \( y = 4 + 3(3) – (3)^2 = 4 + 9 – 9 = 4 \)

(b) Answer: Correct parabola plotted through all points

Plot the points from the completed table and draw a smooth curve connecting them.

The graph should be a downward-opening parabola.

(c) Answer: x ≈ 2.7 to 2.9 and x ≈ -1.9 to -1.7

Find the x-coordinates where the parabola intersects the line y = 2x – 1.

These ranges are the solutions to the equation \( 4 + 3x – x^2 = 2x – 1 \).

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