Function Operations and Composition
g(x) =x3 + x
h(x) = x + 5
Find g(x) + h(x)
x3+2x+5
Find the inverse.
(1, -3), (-2, 3), (5, 1), (6, 4)
(-3, 1), (3, -2), (1, 5), (4, 6)
What is the end behavior of this equation.
y = 6x5 + 4.3x3 + 2.8x +.03
Since the degree is odd and the coefficient is positive, the end behavior is down to the far left and up to the far right.
Solve the Equation
2log8x = -2
1/8
f (x) = x + 5
g(x) =x2 + x
Find f (x) - g(x)
-x2 + 5
Find the inverse.
(-5, 7), (-6, -8), (1, -2), (10, 3)
(7, -5), (-8, -6), (-2, 1), (3, 10)
What is the end behavior of this equation.
y = -2x4 + 5x4 - 3
Since the degree is even and the coefficient is negative, the end behavior is down to the far left and down to the far right.
Solve the Equation
log8n = 2
64
g(t) = t2 + 3t
f (t) = 3t - 4
Find g(t) × f (t)
3t3 + 5t2 - 12t
Find an equation for the inverse
y = 3x + 2
y= (x-2)/3
Graph the Equation.
What are the zero(s) and what is the minimum and maximum?
x3 + 11x2 + 35x + 32
Min = (-2.3 , -2.5 )
Max= (-5 , 7)
Zeros- (-6.2 , 0) (-3.2 , 0) (-1.6, 0)
Solve the Equation
ln(2k + 7) = ln(-k - 8)
No solution
g(x) = -4x + 4
h(x) =x3 + 4x2
Find g(x) × h(x)
-4x4 - 12x3 + 16x2
Find an equation for the inverse
y=-3/4x+5
y= -4/3x + 20/3
Graph the Equation.
What are the zero(s) and what is the minimum and maximum?
f(x)= x2 + 2x -5
Min = (-1,-6)
Max= infinite
Zeros- -3.4 , 1.4
Solve the equation-
log4(b2 + 11) = log4(-10b + 2)
-9, -1
g(t) = 4t - 3
f (t) = t2 - t
Find g(f(t))
t2 - 4t - 3
Find an equation for the inverse
y= x2 - 4
y= + or - √ x+4
Graph the Equation.
What are the zero(s) and what is the minimum and maximum?
x3 + x2 - x - 2
Min = (0.3 , -2.2)
Max= (-1 , -1)
Zeros- (1.2 , 0)
Sophie is buying a used car for $4,500.00. The car is depreciating at a rate of 5% each month
a) Write an equation which models the value of the car after "x" months.
b) How much will the car be worth after 8 months?
c) When will the car's value be $2,000?
a) y = 4500 × 0.95x
b) $2,985.39
c) 15.81 months