Mathematics 4024 · O Level · Graphs of functions

Graphs of functions — practice question

The table underneath gives several values of $x$ together with the matching values of $y$ for $y=\frac{1}{4}\times2^x$.
(a)[1]

Complete the table below.

(b)[2]

Using the grid below, draw the graph of $y=\frac{1}{4}\times2^x$.

(c)[2]

By drawing an appropriate line, find the gradient of the graph at $x=4$.

(d(i))[1]

Show that the line $2x+y=6$, together with the graph of $y=\frac{1}{4}\times2^x$, may be used to solve the equation $2^x+8x-24=0$.

(d(ii))[2]

Hence, solve $2^x+8x-24=0$.

(e(i))[1]

Determine the gradient of $PQ$.

(e(ii))[1]

On the grid, draw the line $l$, parallel to $PQ$, that touches the curve $y=\frac{1}{4}\times2^x$.

(e(iii))[2]

Write down the equation for $l$.

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