Let f(x) = . Find a formula for a function g whose graph is obtained from f by the given sequence of transformations.
(1) shift left 3 units
(2) vertical stretch by a factor of 2
(3) reflect across the x-axis
(1) the graph of f(x-h) is shifted right by h.
(2) The graph of s*f(x) is stretched by a factor of s.
(3) reflection across the x-axis changes f(x) to -f(x).
Now apply these rules to your mystery function.
Why did the function go to the party? Because it wanted a good transformation!
To obtain the function g(x) from f(x) by the given sequence of transformations, we can apply each transformation step by step.
(1) Shifting left 3 units: To shift the function left 3 units, we need to replace x with (x + 3) in f(x). So, g(x) = f(x + 3).
(2) Vertical stretch by a factor of 2: To vertically stretch the function by a factor of 2, we need to multiply the function by 2. So, g(x) = 2 * f(x + 3).
(3) Reflect across the x-axis: To reflect the function across the x-axis, we need to multiply the function by -1. So, g(x) = -2 * f(x + 3).
Therefore, the formula for the function g(x) is g(x) = -2 * f(x + 3).
To find the formula for the function g(x) after the given sequence of transformations, we can follow these steps:
Step 1: Start with the original function f(x).
Step 2: Shift f(x) left 3 units.
Step 3: Apply a vertical stretch to the shifted function.
Step 4: Reflect the stretched function across the x-axis.
Let's go through each step in detail:
Step 1: Start with the original function f(x), which is not specified in the question. Please provide the equation of f(x) for further calculations.
Once we know the equation for f(x), we can proceed with the remaining steps.
To find a formula for the function g(x) after applying the given sequence of transformations to f(x), we can apply each transformation step-by-step.
Step 1: Shift left 3 units
To shift the graph of f(x) left by 3 units, we replace x with (x + 3) in the equation of f(x). So the equation becomes f(x) = sqrt(x + 3).
Step 2: Vertical stretch by a factor of 2
To vertically stretch the graph by a factor of 2, we multiply the entire function by 2. So the equation becomes f(x) = 2 * sqrt(x + 3).
Step 3: Reflect across the x-axis
To reflect the graph across the x-axis, we multiply the entire function by -1. So the equation becomes f(x) = -2 * sqrt(x + 3).
Therefore, the formula for the function g(x) obtained from f(x) by the given sequence of transformations is g(x) = -2 * sqrt(x + 3).