Hint
Use the stated units and precision. Identify the vertical translation of the reciprocal graph.
Worked solution
(a)
Identify the vertical translation of the reciprocal graph.
The term \(\displaystyle \frac{8}{x}\) tends to zero for large |x|, leaving 3.
Answer: \(3\)
(b)
Evaluate the complete function at the permitted input.
\(11\) follows by substituting \(\displaystyle x=1\).
Answer: \(11\)
(c)
Set the output to zero and preserve the excluded input.
Solving \(\displaystyle 3 + \frac{8}{x} = 0\) gives \(\displaystyle - \frac{8}{3}\), which is not zero.
Answer: \(\displaystyle - \frac{8}{3}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Identify the vertical translation of the reciprocal graph.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Evaluate the complete function at the permitted input.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Set the output to zero and preserve the excluded input.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.