Hint
Use the stated units and precision. Read the vertical translation and identify the unattained limiting output.
Worked solution
(a)
Read the vertical translation and identify the unattained limiting output.
The exponential term tends to zero as x tends to negative infinity, leaving 2.
Answer: \(2\)
(b)
Evaluate the zero power before multiplying and translating.
The zero power is 1, so the output is 3.
Answer: \(3\)
(c)
Substitute into the complete exponential function.
Multiply 1 by 2, then add 2, giving 4.
Answer: \(4\)
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: Read the vertical translation and identify the unattained limiting output.
- 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 zero power before multiplying and translating.
- 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: Substitute into the complete exponential function.
- 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.