On the grid, sketch the curve with equation $y = 2^x$ - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 2

To sketch the curve of the equation $y = 2^x$, we note that this is an exponential function.

1. Identify key features of the graph:

   • The graph approaches the x-axis (y=0) as $x$ approaches negative infinity but never touches it, indicating a horizontal asymptote at y=0.
   • At $x=0$, $y=2^0=1$, so the point (0,1) is on the graph.
   • As $x$ increases, $y$ increases rapidly since $2^x$ grows exponentially.

2. Points of intersection with the axes:

   • The graph intersects the y-axis at the point (0,1) where $y=2^0=1$.
   • The graph does not intersect the x-axis because $y=2^x$ is never zero for any real number $x$.

Thus, the coordinates of intersection with the axes are:

• Point of intersection with the y-axis: (0,1)
• No intersection with the x-axis.