Linear Functions
Find the slope of a line passing through f(2) = 1 and f(4) = 5
Slope (m) = 2
What is the vertex of f(x) = 3(x+1)2 -5 ?
Vertex: (-1,-5)
Is f(x) = 5x3 + 2x1/2 -1 a polynomial?
No - no fraction exponents
List all the possible rational zeros (p/q list) for f(x) = 2x3 -3x2 +x -6
+/- 1, 2, 3, 6, 1/2, 3/2
Find the x and y intercepts of f(x) = (x-5)/(x+2)
x-intercept: (5,0)
y-intercept: (0, -2.5)
Find the slope AND y-intercept of a line passing through (0,8) and (2,4)
Slope (m) = -2
y-intercept: (0,8)
Describe all transformations from f(x) = x2 to f(x) = 2(x-1)2 + 3
Vertical Stretch, shift right 1, shift up 3
What is the degree and leading coefficient of f(x) = 3x4 - 5x2 + x - 9 ?
Degree: 4
Leading Coefficient: 3
Divide using any method: (x3 + 5x2 + 5x - 2) / (x+2)
x2 + 3x - 1
Find the vertical and horizontal asymptotes of f(x) = (3x+1)/(x-4)
Vertical Asymptote: x = 4
Horizontal Asymptote: y = 3
Write the equation of a line in slope-intercept form for the line such that f(1) = 10 and f(3) = 4
f(x) = -3x + 13
What is the vertex of f(x) = -(x+2)2 ?
Vertex: (-2, 0)
Describe the end behavior of f(x) = -x5 + 2x2 -1
Left (-infinity) = + infinity
Right (+infinity) = - infinity
Divide using any method (2x3 - 4x + 1) / (x-1)
2x2 + 2x - 2 + -1/(x-1)
Find the vertical and horizontal asymptotes of
f(x) = (x+1)/(x2 -x -6)
Vertical Asymptotes: x = 3
Horizontal Asymptote: y = 0
Write the equation of the line in slope-intercept form such that f(-1) = 2 and f(3) = 3
f(x) = 1/4x + 9/4
or
f(x) = 0.25x + 2.25
Describe all transformations from f(x) = x2 to f(x) = -0.5(x+4)2
Reflection over the x-axis
Vertical shrink
Shift left 4
Describe the end behavior of f(x) = 7x6 +x -10
left (-infinity) = + infinity
right (+infinity) = + infinity
Find all zeros of f(x) = x3 - 4x2 + x + 6
x = -1, 2, 3
Find the vertical asymptote(s) and hole(s) for
f(x) = (x+2)(x-3)/(x+2)
Vertical Asymptote(s): NONE
Hole(s): (-2, y)
Write the equation of the line that passes through (1,5) and is parallel to the line f(x) = -2x + 1
Write the equation of a parabola with a reflection over the x-axis, vertical shrink by 1/4, shifted up 3.
f(x) = -1/4 x2 +3
Write an equation for a 5th degree polynomial with a leading coefficient of -3 and 4 terms.
f(x) = -3x5 + ____ + _____ + ______
Divide using long division: (2x3 + 5x2 - x + 1) / (x2 + x - 1)
2x + 3 + (-2x+4)/(x2 +x-1)
Create a rational equation with a vertical asymptote at x = 1 and an x-intercept at x = -3
f(x) = (x+3)/(x-1)