Evaluations
If f(x) = 3x2 - 5x + 4, find f(-2)
f(-2) = 26
Determine the domain and range of the following function: y = x2 - 4
D: All real numbers
R: [ -4 , infinity)
If f(x) = sqrt(x-1) and g(x) = x2 + 2, what is f(g(x))?
f(g(x)) = sqrt(x2 +1)
Write out a function for the price of a new car after a 5% discount and a $400 rebate.
What would be the sale price of a car that originally cost $43,500?
f(x) = 0.95c - 400
f(43500) = $40925
Where is the axis of symmetry for the function
y = (x - 2)(x + 1)?
At x = 1/2
If f(x) = (2x + 1)1/2, find f(4)
f(4) = 3
f(x) = sqrt(1-x)
Determine the domain and the range.
D: ( - infinity, 1]
R: [0 , infinity)
If a ball is thrown upward from an initial position of 3.5 feet at a speed of 48 feet per second, what is the maximum height the ball will reach?
39.5 feet
Write out the quadratic function that has been shifted 3 units down, 5 units to the right, stretched by half and reflected across the y-axis.
y = 1/2 (-x - 5)2 - 3
Find the vertex for the function:
y = 2x2 + 8x + 7
v: (-2, -1)
If the point (-2x, 3y) resides in Quadrant III, in what quadrant is the point (3x, -2y)?
Quadrant I
Find the midpoint between (-2, 3) and (5, -4)
( 3/2, -1/2 )
If f(x) = 5x2 + 4x - 1, find the zeros of the function.
zeros: x = 1/5, -1
Transform the absolute value function by shifting 2 units to the left, 4 units up, and reflecting across the x-axis.
y = -abs(x + 2) + 4
Determine the vertex and the axis of symmetry for the parabola:
y = -3x2 + 6x - 4
V: (1, -1)
axis: x = 1
f(x) = x2 - 4x + 1, find the difference quotient of f.
2x + h - 4
Find the distance between (-2, 6) and ( 4, -3 )
3 x sqrt 13
Find the average rate of change of the function,
y = x3 + 2x + 1 , from x = 1, x = 3
Average rate of change = 15
Pressure, volume, and temperature are all related. Pressure varies inversely with volume and directly with temperature.
When P = 30 psi, volume = 42.5, and temperature = 15 degrees. What is pressure when volume drops to 35, and temperature increases to 25?P = 60.71 psi
Write out the equation for the parabola with vertex
(1, 2) that passes through the point (3, -6)
y = -2(x - 1)2 + 2
If f(x) = x3 - 1, what is the inverse function for f?
f-1(x) = (x+1)1/3
Find the equation of the line that passes through the given point and is perpendicular to the given line.
5x - 4y = 8, (3, -2)
y = - 4/5 x + 2/5
Sketch the graph of the following piece-wise function:
y = -3x + 5, x is less than -1
x2 - 4, x is greater than -1
(Graph on graph board)
Find the inverse function for f(x) = (2x - 1)/((x+4)
f-1(x) = (4x+1)/(2-x)
A rancher has 400 feet of fencing to enclose two adjacent rectangular corrals. Write out an equation for the area of the two corrals. DRAW!
A = [8x(100 - x)]/3