Mathematics

Mathematics

Problem

For the exponential function h(x)=2 x−1−4h(x)=2^{\,x-1}-4, 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 x=0x=0. For the x-intercept, you're finding where it crosses the horizontal axis—that's when y=0y=0. 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 x=0x=0. For the x-intercept, you're finding where it crosses the horizontal axis—that's when y=0y=0. 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.

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