Write an equation for a function that has a graph with the given characteristics.
The shape of y=^3 squareroot x is shifted 7.3 units to the left. This graph is then vertically stretched by a factor of 9. Finally, the graph is reflected across the x-axis.
Thanks
parent: y = ∛x
shift left 7.3 gives y = ∛(x+7.3)
stretch by 9 gives y = 9∛(x+7.3)
reflection changes the sign of the y-values, so
y = -9∛(x+7.3)
square root is a particular function.
cube root is not "^3 squareroot"
Try saying
cube root
4th root
5th root
etc. instead of that clunky attempt.
To create an equation for the given characteristics, let's break down each step:
1. Start with the function y = √x.
2. Shift the graph 7.3 units to the left: Replace x with (x + 7.3). This gives us y = √(x + 7.3).
3. Vertically stretch the graph by a factor of 9: Multiply the entire equation by 9. Now we have y = 9√(x + 7.3).
4. Reflect the graph across the x-axis: Multiply the equation by -1. The final equation is y = -9√(x + 7.3).
Therefore, the equation for a function that has a graph with the given characteristics is y = -9√(x + 7.3).
To write an equation for the function with the specified characteristics, let's break down the transformations step by step.
1. Shifting 7.3 units to the left:
To shift the graph of a function to the left, we need to subtract the amount we want to shift from the x-value (inside the square root). So, in this case, we subtract 7.3 from the x-value.
2. Vertically stretching by a factor of 9:
To vertically stretch a function, we multiply the function by the desired stretch factor. In this case, we want to stretch the function by a factor of 9, so we multiply the entire function by 9.
3. Reflecting across the x-axis:
To reflect a function across the x-axis, we change the sign of the entire function. So, if the function was originally positive, it becomes negative, and vice versa.
Combining these transformations, we start with the function y = √x. Applying them step by step, we get:
1. Shifted 7.3 units to the left: y = √(x + 7.3)
2. Vertically stretched by a factor of 9: y = 9√(x + 7.3)
3. Reflected across the x-axis: y = -9√(x + 7.3)
Therefore, the equation of the function with the specified characteristics is y = -9√(x + 7.3).