Review question

# When does this exponential function equal this linear one? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8013

## Suggestion

Draw the graph of $y=3^x$ for values of $x$ from $-2$ to $+2$, plotting at least nine points. [Take $\quantity{2}{cm}$ as unit on the axis of $x$, and $\quantity{1}{cm}$ as unit on the axis of $y$.]

Use your graph to find

1. the roots of the equation $3^x=3x+2$,
2. the range of values of $k$ for which the equation $3^x=kx$ has no real roots.

Can you think of a way to consider the equation $3^x=3x+2$ in terms of two intersecting curves?

Can you use the graphs you sketch to help solve this equation?