Start with the graph of 𝑓(𝑥)=4𝑥. Then write a function that results from the given transformation.Shift 𝑓(𝑥) 7 units left
Question
Start with the graph of 𝑓(𝑥)=4𝑥. Then write a function that results from the given transformation.Shift 𝑓(𝑥) 7 units left
Solution
The function that results from shifting the graph of 𝑓(𝑥)=4𝑥 7 units to the left is 𝑓(𝑥)=4(𝑥+7).
Here's the step-by-step explanation:
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The original function is 𝑓(𝑥)=4𝑥. This is a linear function with a slope of 4.
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To shift the graph of a function to the left by a certain number of units, you add that number to the x in the function. This is because moving to the left on a graph is equivalent to decreasing the x-value, so adding to the x in the function actually moves the graph in the opposite direction.
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Therefore, to shift the graph 7 units to the left, you add 7 to the x in the function, resulting in the function 𝑓(𝑥)=4(𝑥+7).
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