Question

explore transformations of the basic exponential function \\(y = 2^x\\), shown right. first, change the slider for \\(h\\) to positive values such as 1, 2, or 3. the curve shifts \\(h\\) units right.

if \\(h\\) is instead negative, the curve shifts

Explanation:

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<reasoning>

Analyze the transformation equation

Using the Horizontal Translation and Exponential Function Graphs knowledge points
\[
y = 2^{(x-h)} + k
\]

Determine the effect of a negative parameter

Using the Horizontal Translation knowledge point
\[

$$\begin{aligned} &\text{For } h < 0 \text{ (negative value):}\\ &x - h = x - (-|h|) = x + |h|\\ &\text{This shifts the graph to the left.} \end{aligned}$$

\]
</reasoning>

<answer>
If \(h\) is instead negative, the curve shifts <blank>left</blank>.
</answer>

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"Mathematics",
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Answer:

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<reasoning>

Analyze the transformation equation

Using the Horizontal Translation and Exponential Function Graphs knowledge points
\[
y = 2^{(x-h)} + k
\]

Determine the effect of a negative parameter

Using the Horizontal Translation knowledge point
\[

$$\begin{aligned} &\text{For } h < 0 \text{ (negative value):}\\ &x - h = x - (-|h|) = x + |h|\\ &\text{This shifts the graph to the left.} \end{aligned}$$

\]
</reasoning>

<answer>
If \(h\) is instead negative, the curve shifts <blank>left</blank>.
</answer>

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"Mathematics",
"Algebra",
"Exponential Function Transformations"
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