Write an equation for a function that has a graph with the given transformations.
-The shape of 2 is vertically stretched by a factor of 10, and the resulting graph is reflected across the x-axis.

Question

Write an equation for a function that has a graph with the given transformations.
-The shape of  2 is vertically stretched by a factor of 10, and the resulting graph is reflected across the x-axis.

Quizplus · Accepted Answer

Let f(x) be the original function.
- Vertically stretched by a factor of 10: g(x) = 10f(x)
- Reflected across the x-axis: h(x) = -g(x) = -10f(x)
Combining the two transformations: h(x) = -10f(x) The vertical stretching means the function is multiplied by 10, which is represented by the coefficient in front of the function. The reflection across the x-axis means the graph is flipped upside down, which is represented by the negative sign in front of the function. 
Therefore, the equation would be: 
-f(x) = -10*2^(x) 
simplifying,
f(x) = 10*2^(x)

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