Sketch the graph of $y = 3^{x}$ - OCR - GCSE Maths - Question 17 - 2019 - Paper 4

To sketch the graph of the exponential function $y = 3^{x}$, we will evaluate a few key points:

1. Identify key points:

   • When $x = 0$: $y = 3^{0} = 1$
   • When $x = 1$: $y = 3^{1} = 3$
   • When $x = -1$: $y = 3^{-1} = \frac{1}{3} \approx 0.33$

2. Dominant behavior:

   • As $x \to \infty$, $y \to \infty$.
   • As $x \to -\infty$, $y \to 0$.

3. Y-intercept: The y-intercept occurs when $x = 0$, which gives a value of 1.

4. Drawing the curve: Draw a smooth curve through the points $(-1, \frac{1}{3})$, $(0, 1)$, and $(1, 3)$. The curve should approach the x-axis but never touch it as $x$ decreases and rise steeply as $x$ increases.