A function f is given and the indicated transformation are applied to its graph (in the given order) write the equation for the final transformed graph
F(x)=x^2 stretch vertically by a factor of 3 shift downward 4 units and shift 2 units to the right
The equation for the final transformed graph is:
g(x) = 3(x - 2)^2 - 4
To find the equation for the final transformed graph, we need to apply the given transformations in the given order to the original function f(x) = x^2.
1. Vertical Stretch by a Factor of 3:
To stretch the graph vertically by a factor of 3, we multiply the function by 3. Thus, the new function becomes F1(x) = 3x^2.
2. Shift Downward 4 Units:
To shift the graph downward by 4 units, we subtract 4 from the function. Thus, the new function becomes F2(x) = 3x^2 - 4.
3. Shift 2 Units to the Right:
To shift the graph 2 units to the right, we replace x with (x - 2) in the function. Thus, the final transformed graph equation becomes F(x) = 3(x - 2)^2 - 4.
Therefore, the equation for the final transformed graph is F(x) = 3(x - 2)^2 - 4.
To write the equation for the final transformed graph, we need to apply the given transformations to the original function F(x) = x^2 in the correct order.
Firstly, let's understand the effects of each transformation:
1. Stretch vertically by a factor of 3: This means that the y-values on the graph will be multiplied by 3.
2. Shift downward 4 units: This means that the entire graph will be shifted downward by 4 units along the y-axis.
3. Shift 2 units to the right: This means that the entire graph will be shifted 2 units to the right along the x-axis.
Now, let's apply these transformations step by step to the original function F(x) = x^2:
1. Stretch vertically by a factor of 3: Multiply the function by 3. The new function becomes F(x) = 3 * x^2.
2. Shift downward 4 units: Subtract 4 from the function. The new function becomes F(x) = 3 * x^2 - 4.
3. Shift 2 units to the right: Replace x with (x - 2) in the function. The new function becomes F(x) = 3 * (x - 2) ^ 2 - 4.
Therefore, the equation for the final transformed graph is F(x) = 3 * (x - 2) ^ 2 - 4.