What does the transformation f(x)↦f(-x) do to the graph of f(x)?
1 answer:
The function will simply get reflected about the y-axis.
Let's approach this through what we know. Since we know that the x values are mirrored, we know that the points in Quadrant I and IV will be reflected over to the negative side, Quadrants II and III, because they simply change in signs.
However, we also know that the function y-values do not change. This is because whatever the x values are don't change the range and y-values of an even function.
To be more specific, if we have an even function, we are most likely dealing with quadratics or variants/transformations of the quadratic function.
If we were to have 2, and -2, and we wanted to plug them into the equation:
, the signs do not change the y-values of the function.
Hence, we know that it ONLY gets reflected across the y-axis.
Let's approach this through what we know. Since we know that the x values are mirrored, we know that the points in Quadrant I and IV will be reflected over to the negative side, Quadrants II and III, because they simply change in signs.
However, we also know that the function y-values do not change. This is because whatever the x values are don't change the range and y-values of an even function.
To be more specific, if we have an even function, we are most likely dealing with quadratics or variants/transformations of the quadratic function.
If we were to have 2, and -2, and we wanted to plug them into the equation:
Hence, we know that it ONLY gets reflected across the y-axis.
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Answer:
Step-by-step explanation:
When comparing to standard form of a parabola:
Vertex form of a parabola is: , which is what we are trying to convert this quadratic equation into.
To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: .
Substitute in -8 for b and 2 for a.
Simplify this fraction.
The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.
Simplify.
We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).
Step-by-step explanation:
The given equations are :
y=-x+2 ....(1)
y = -4x +7 ....(2)
From equation (1) and (2)
-x+2 = -4x +7
Taking like terms together
-x+4x=7-2
3x = 5
x = 1.667
Put the value of x in equation (1)
y=-(1.667)+2
y = 0.333
The solution of the equations are (1.667,0.333). The attached figure shows the graph for the equations.
