How would I write this as a function of y=x^3
Reflected in the y axis, horizontally stretched by a factor of 7, vertically translated 19 units down.
Would this be correct?
g(x)= (-1/7(x-1))^3-19
For a reflection about the y-axis, replace x by -x.
For stretching horizontally, replace x by x/7.
Translate vertically k units up, add k to the function.
You have done the vertical translation correctly.
Can you give it another try, you're not far?
To write the function for the given transformations, let's break it down step-by-step:
1. Reflected in the y-axis:
When a function is reflected in the y-axis, the x-values change their sign. In this case, we have y = x^3, and the reflection would be y = (-x)^3.
So, we have y = (-x)^3.
2. Horizontally stretched by a factor of 7:
To horizontally stretch a function, we multiply the x-values by the stretching factor. In this case, the function is y = (-x)^3, and we want to stretch it by a factor of 7.
To do the stretching, the function becomes y = (-7x)^3.
So, we have y = (-7x)^3.
3. Vertically translated 19 units down:
To vertically translate a function, we add or subtract a constant value from the function. In this case, the function is y = (-7x)^3, and we want to translate it 19 units down.
To translate it down, the function becomes y = (-7x)^3 - 19.
So, the final transformed function is y = (-7x)^3 - 19.
Based on the given transformations, the function you wrote, g(x) = (-1/7(x-1))^3-19, is not correct.
The correct function would be g(x) = (-7x)^3 - 19.
To write the function that represents the given transformation, let's break it down step by step:
1. Start with the original function: y = x^3
2. Reflection in the y-axis: This means that any positive value of x will become negative, and vice versa. To reflect a function in the y-axis, you change the sign of x in the equation. So, replace x with -x:
y = (-x)^3
3. Horizontal stretch by a factor of 7: To horizontally stretch a function, you need to multiply x by a constant. In this case, the factor is 7. So, multiply -x by 7:
y = (-7x)^3
4. Vertical translation 19 units down: This means that the entire graph will shift down by 19 units. To achieve this, you subtract 19 from the equation:
y = (-7x)^3 - 19
So, the correct function for the given transformation would be:
g(x) = (-7x)^3 - 19
The function you provided, g(x) = (-1/7(x-1))^3 - 19, seems to have an incorrect reflection in the y-axis and an additional horizontal shift to the right by 1 unit.