Mathematics
Mathematics
Problem
For the exponential function , find (i) the y-intercept, and (ii) the x-intercept.Intuitive explanation
The key is recognizing that intercepts are just special points where the graph crosses the axes. For the y-intercept, you're finding where the curve meets the vertical axis—that's when . For the x-intercept, you're finding where it crosses the horizontal axis—that's when . Both require simple substitution and solving, but the x-intercept will need you to isolate the exponential term and use logarithms or recognize a power of 2.
Intuitive explanation
The key is recognizing that intercepts are just special points where the graph crosses the axes. For the y-intercept, you're finding where the curve meets the vertical axis—that's when . For the x-intercept, you're finding where it crosses the horizontal axis—that's when . Both require simple substitution and solving, but the x-intercept will need you to isolate the exponential term and use logarithms or recognize a power of 2.