<p>the graph of y=h(x) is shown above.Which of the following could be the graph of y=h(2x)?</p>
<p>for the graph of y=h(x) the y coordinates are at (0,2) and the x are at(-2,0) so what will be the coordinates of y=h(2x) thanks</p>
<p>Can you post the picture up?.. I’m confused.</p>
<p>for the graph of y=h(x) the graph cuts the y axis at (0,2) and the x axis at (-2,0) so what will be the coordinates of y=h(2x).i cant post up the picture.the answer is that the x-axis coordinate will shift one unit to the right that is its coordinate will now be (-1,0).how do you arrive at this answer?</p>
<p>Well the slope is 1 in y=h(x), and when you double the slope the x intercept in cut into half, and the y intercept does not change.</p>
<p>Here’s how you can do it by plugging in the given points:</p>
<p>You are given that h(0)=2 and h(-2)=0 (this is the same as saying (0,2) and (-2,0) are on the graph.</p>
<p>Plugging in to g(x)=h(2x) we have g(0)=h(2*0)=2 and g(-1)=h(2(-1))=0. So (0,2) and (-1,0) are on the graph of g(x)=h(2x).</p>
<p>Another method using transformations:</p>
<p>For c>0, f(cx) is a contraction or expansion of f(x) in the horizontal direction. If c>0 it is a contraction. For 0<c<1 it is an expansion. </p>
<p>In this problem h(2x) is a contraction by a factor of 2. So all x-values will be halved (while the corresponding y-values remain the same).</p>
<p>Remark: If you are going for an 800, you should review the 8 basic transformations:</p>
<p>shift up f(x)+c
shift down f(x)-c
shift left f(x+c)
shift right f(x-c)
reflection in x-axis -f(x)
reflection in y-axis f(-x)
vertical expansion/contraction cf(x)
horizontal contraction/expansion f(cx)</p>
<p>Very nice review! Thanx DrSteve!!</p>