Mathematical Methods — Question 5

QCAA 2025, Paper 2 · 1 mark

Q5 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 5

Which statement best describes a feature of the graph of the exponential function

y=e^x

x\in\mathbb R

(A)

\displaystyle\lim_{x\to\infty}e^x=e

(B)

When

x=0

y=e

(C)

The graph has an asymptote with the equation

x=0

(D)

The gradient of the graph has the same value as the function at all points on the graph.

ABCD

WORKED SOLUTION

1 mark

ANSWER

D — The gradient of the graph has the same value as the function at all points on the graph.

Worked solution

Since

\frac{d}{dx}e^x=e^x

, the gradient equals the function value at every point; option D.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.