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100
y=(x-c)²
"c" moves the function right across the x-axis
100
y = (3x)²
based on the parent function, the function will be horizontally compressed by a factor of 3. Each point on this compressed function will now be one third the distance from the y-axis as its corresponding point on the original function
100
y=(x+c)²
"c" moves the function left across the x-axis
100
y=-(x)
reflection over the x-axis, same x-values create opposite y values
100
y=-(x)
reflection over the x-axis, same x-values create opposite y values
200
y=|x|
200
y=√(x+3)
the function moves left along the x-axis 3 units from its parent function
200
y=-√(x+2)+4
reflected over the x-axis, left two units along the x-axis, up 4 units on the y-axis from its parent function
200
y=(x+3)³-2
the function will move left 3 units along the x-axis and down two units on the y-axis from its parent function
200
y = (1/3x)²
based on the parent function, the function will be horizontally stretched by a factor of 3. Each point on this stretched function will now be 3 times as far from the y-axis as its corresponding point on the original function
300
y= |½x|
y= |½x|
based on the parent function, the function will be horizontally stretched by a factor of 2. Each point on this stretched function will now be twice as far from the y-axis as its corresponding point on the original function
300
y= |2x|
based on the parent function, the function will be horizontally compressed by a factor of 2. Each point on this compressed function will now be half the distance from the y-axis as its corresponding point on the original function
300
y = -[-3(x + 8)]²
Reflect the function f(x) = x2 in the x-axis and the y-axis, compress horizontally by a factor of ¹/₃, and translate left 8 units
300
Completing the square
Divide the first two terms by the "a" coefficient. Bracket the results, place GCF in front of brackets. Divide the original "b" coefficient by 2, square the answer, add the positive answer after the "bx" value of the trinomial and place the same answer with the negative sign after the "c" value; if applicable, multiply this number by the greatest common factor, the coefficient in front of the first two terms. Bracket and factor the new trinomial and collect like terms for the numbers outside the trinomial.
300
y=3f[½(x+4)]+7
A function with a vertical stretch of 3, horizontal stretch by factor 2, shifted left 4 and up 7
400
y = -¼(x-4)³
Reflect the function f(x) = x³ in the x-axis, compress vertically by a factor of ¼ , and translate right 4 units.
400
y = 4[-(x+7)]³
Reflect the function f(x) = x³ in the y-axis, stretch vertically by a factor of 4, and translate left 7 units.
400
|½(x - 8)| - 7
The equation of the function graphed in this picture
400
How do you multiply mixed radicals together?
Multiply the "a" values like regular multiplication, and the "x" or radicand values together like regular values. Put the multiplied "a" value to the left of the radical sign and the radicand or the "x" value to the right of the radical sign. Radicand numbers must be equal or greater than 0.
400
How do you divide radicals?
Treat the radicals like as if they're whole numbers. Value of "a" must be equal or greater than 0, but the value of the radicand or "x" must be greater than 0. Ex: √56/√8 turns into √7.
500
y = [¹/₃(x-5)]³ + 2
The equation of the function graphed in this picture
500
What is the discriminant?
What is the discriminant?
The value of b^2-4ac. When b^2-4ac is greater than 0, the equation has 2 real roots, or zeros. When b^2-4ac is the value 0, there is only one zero. When b^2-4ac is less than 0, there are no real roots.
500
Explain Inverse of a function and make an example. Are they always a function?
Is a relation that reverses the x and y values of the original function.
Graphically: it is a reflection around the line y=x
F(x) becomes F^-1(x)
Example: y=3x+2 becomes x=3y+2
inverses of a function are not always functions themselves
only in vertex form
500
How can you find the transformation of asymptote?
Look for the horizontal translation to left/right and vertical translation up/down
500
How do you graph a rational function?
Sketch the asymptotes first. Plot (1, 1) and (-1, -1). The graph will be actually 2 lines, each going through the points and hugging the asymptotes.