2023HSCQ8The diagram shows the graph of a function. [Graph of the function] Which of the following is the equation of the function? A. y=∣1−∣∣x∣−2∣∣y=\left|1-\left||x|-2\right|\right|y=∣1−∣∣x∣−2∣ B. C. D.
2023HSCQ9The graph of a cubic function, y=f(x)y=f(x)y=f(x), is given below. [Graph of the cubic function y=f(x)y=f(x)y=f(x)] Which of the following functions has an inverse relation whose graph has more than 3 points with an xxx-coordinate of 111? A. y=f(x)y=\sqrt{f(x)}y=f(x) B. y=1f(x)y=\dfrac{1}{f(x)}y=f(x)1 C. y=f(∣x∣)y=f(|x|)y=f(∣x∣) D. y=∣f(x)∣y=|f(x)|y=∣f(x)∣1 markMultiple choice
2023HSCQ11 (a)The parametric equations of a line are given below. x=1+3ty=4t\begin{aligned} x&=1+3t\\ y&=4t \end{aligned}xy=1+3t=4t Find the Cartesian equation of this line in the form y=mx+cy=mx+cy=mx+c.2 marksShort answer
2023HSCQ14 (a) (i)Let f(x)=2x+lnxf(x)=2x+\ln xf(x)=2x+lnx, for x>0x>0x>0. (i) Explain why the inverse of f(x)f(x)f(x) is a function.1 markShort answer
2023HSCQ14 (a) (ii)Let f(x)=2x+lnxf(x)=2x+\ln xf(x)=2x+lnx, for x>0x>0x>0. (ii) Let g(x)=f−1(x)g(x)=f^{-1}(x)g(x)=f−1(x). By considering the value of f(1)f(1)f(1), or otherwise, evaluate g′(2)g'(2)g′(2).2 marksShort answer