Question5. DETAILS
MY NOTES
OSCOLALG1 6.2.094.
Graph the transformation of .
Studdy Solution
STEP 1
1. The function is an exponential function with base 6.
2. The function is a transformation of .
3. The transformation involves a reflection across the y-axis.
STEP 2
1. Identify the parent function and its graph.
2. Determine the transformation applied to the parent function.
3. Graph the transformed function .
STEP 3
Identify the parent function and its graph.
The parent function is . This is an exponential function that passes through the point and increases rapidly as increases. The graph is a smooth curve that approaches the x-axis as decreases (but never touches it), and rises steeply as increases.
STEP 4
Determine the transformation applied to the parent function.
The function is a transformation of . The transformation involves replacing with , which reflects the graph of the function across the y-axis. This means for every point on the graph of , there is a corresponding point on the graph of .
STEP 5
Graph the transformed function .
1. Start by plotting the key point of the parent function , which is . This point remains unchanged because reflecting across the y-axis does not affect points on the y-axis.
2. Reflect other key points of across the y-axis. For example, if , then . Similarly, if , then .
3. Draw a smooth curve through these points, ensuring the graph approaches the y-axis as increases and decreases, but never touches it.
The graph of is a decreasing exponential function that approaches the x-axis as increases and rises steeply as decreases.
The transformation has been graphed successfully.
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