- when x is replaced with -x in the equation of a function y= f(x), it'll be the reflected in the y axis.
- when y is replaced with -y in the equation of a function y= f(x), its graph is reflected in the x- axis.
- when interchanged with y in the equation of a function y = f(x), it's reflected in the mirror line y=x. this is called inverse function.
- when x is interchanged with y in the equation of a function y = f (x), it's reflected in the mirror line y = x.
FINDING THE INVERSE EQUATION STEPS:
- Replace f(x) with y
- Switch x and y
- solve for y
- Replace y with f^-1 (x)
eg/ f(x) = 2x + 2 > linear
y = 2x + 2 > change " f(x)" to "y"
x = 2y + 2 > switch x and y
x - 2 = 2y > bring the +2 to the left side, that makes it -2
x - 2 = 2y > divide both sides by 2.
2 2
y = 1/2x - 1 > inverse function
GENARALIZING REFLECTIONS
transformation effects on graph
- f (x) reflection in x- axis
f (- x) reflection in y- axis
f ^ -1 (x) reflection in y = x
SYMMETRY
even value
f(-x) > means x is negative and y is positive. QII
f(x) > means that x and y are both positive. QI
-f(-x) > means that x and y are both negative. QIII
-f(x) > means that x is positive and y is negative. QIV
odd value
f(-x) > means that x is negative and y is positive. QII
-f(x) > means that x is positive and y is negative. QIV
f(x) > means that x and y are both positive. QI
-f(-x) > means that x and y are negative. QIII
DETERMINING IF A SHARE IS A FUNCTION
there are two test to check, one is the vertical line test (VLT) and the horizontal line test (HLT).
*do the vlt first then the hlt
VLT - if a vertical line test crosses through the graph only once, then the graph is a function.
HLT - if a horizontal line crosses through the graph only one and it has passed VLT then the graph is a one to one function.
* function - for all the value x, only 1 y value.
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