1.1 - Functions and Function Notation
True or False: A graph can fail the vertical line test and still represent a function.
False
Find the average rate of change given these points: (0,6) and (25,30)
24/25
Which equation has the greater slope?
Equation 1 : y = 2 + 15x
Equation 2: y = 7x - 9
Equation 1
Find a formula for the linear function passing through the points (-2,14) and (1,-1).
y = -5x + 4
Write the following relationship using function notation (y=f(x)). Number of molecules, n, in a gas, is a function of the volume of the gas, g.
n=f(g)
Find the average rate of change of f(x)= 2x^2 + 1 between the points (2,9) and (4,33).
Avg rate of change = 12
P(t) = 4798 - 3/4(t)
Vertical intercept = ?
Slope = ?
Vertical intercept = 4798
Slope = -3/4
Is the given function linear?
P(v) = -3(v^4) - 14
No because the power of v is not 1
x = 0 | 1 | 2 | 3 | 4
f(x)= 1 | 5 | 9 | 10 | 9
f(0)=?
f(?)=10
f(1)=?
f(0) = 1
f(3) = 10
f(1) = 5
Give the rate of change:
x = -4 | -2 | 0 | 1
f(x)= 6 | 4 | 2 | 1
Are the lines 5y = 10 - x and 25y = -100 +5x perpendicular/parallel/neither?
Neither
The sales tax on an item is 8%. Express the total cost, C, in terms of the prices of the item, P.
C = P + 0.08P
In 1984, the population of a town was 455 and grew at a constant rate of 30 people per year. Find a formula for P, the town's population, in terms of t, the number of years since 1984.
P = 30t + 455
Find the equation of the line parallel to 4x + 5y = 8 passing through the point (0,8).
y = -4/5(x) + 8
A chemical company spends $2.4 million to buy machinery before it starts producing chemicals. Then it spends $0.2 million on raw materials for each million liters of chemical produced.
Find a formula that expresses the total cost, C, in millions of dollars, as a function of L, the number of million liters produced.
C = 0.2L + 2.4
A new Honda costs $23,500. The car's value depreciates linearly to $18,823 in three years time. Write a formula which expresses its value, V, in terms of its age, t, in years.
V(t) = -1559t + 23500
Line r is given by y = 7 - 2/3(x) and point M has coordinates (6,5). Find the equation of the line containing M and perpendicular to r.
y = 3/2(x) - 4