Determine which pattern the data follows. Identify the type of function that has the pattern.
x: 1, 3, 5, 7, 9
y: 352, 136, 64, 136, 352
Constant second differences property. Quadratic.
100
Use the definition of logarithm to write x as a logarithm. Then evaluate the logarithm by calculator and show that raising 10 to that power gives a result that agrees with the given equality.
0.00321 = 10^x
x = log(0.0321) = -1.4934
100
Which property do logarithmic functions have?
Multiply- add
100
Draw the reference angle for an angle whose terminal position lies in each of the 4 qudrants.
Check for correctly drawn reference angles: Does your reference angle lie between the terminal position and the nearest horizontal axis? Does your reference angle go in a counterclockwise direction?
200
Name the function and give its general equation.
Quadratic equation. y=a*x^2 + bx + c
200
Describe the effect on f(x) if you double the value of x.
a. Direct square power function
b. Direct fourth power function
c. Inverse square variation power function
a. Mutiply y by 4
b. Multiply y by 16
c. Divide y by 4
200
Demonstrate numerically the properties of logarithms. Then explain how the result agrees with the definition of logarithm.
log(1/7) = -log(7)
log (1/7) = -0.8450 = -log(7); 1/7= 10^(-0.8450)
200
Suppose that f is a natural logarithmic function with values f(3.6)=1 and f(921.6)= 5. Determine the particular equation.
y = 0.0760 + 0.7213lnx
200
Sketch an angle of 7321 degrees, mark its reference angle, and find the measure of the reference angle.
angle is in second quadrant. Theta_ref = 50 degrees
300
Power functions and exponential functions both have exponents. What major algebraic difference distinguishes these two types of functions?
In power functions, the exponent is constant and the independent variable is in the base. In exponential functions, the base is constant and the independent variable is in the exponent.
300
The add-multiply property proof problem: Prove that for an exponential function, adding a constant to x multiplies the corresponding value of f(x) by a constant.
Do this by showing that if x_2= c + x_1, then f(x_2) equals a constant times f(x_1).
Hint: Start by writing the equations of f(x_1) and f(x_2), and then make the appropriate substitutions and algebraic manipulations.
see instructor
300
Solve the equation algebraically and check your solution.
log_2(2x-1) - log_2(x+2) = -1
x = 4/3
300
What is the general equation for a logarithmic function?
y= a+b*log_c(x)
300
What does it mean if an angle is in standard position?
1. Its vertex is at the origin.
2. Its initial side is along the positive horizontal axis.
3. It is measured counterclockwise from the horizontal axis if the measure is positive and clockwise if the angle is negative?
400
What graphical feature do quadratic functions have that linear, exponential, and power functions do not have?
Quadratic functions have either a maximum or minimum point. Exponential, linear, and many power functions do not have these (certain power functions have a minimum point at the origin).
400
Given that f(x) varies exponentially with x and that f(1)=100 and f(4)=90, find f(7), f(10) and f(16).
f(7)=81, f(10)=72.9, f(16)=59.049
400
Find the missing values.
a. ln(e)= ?
b. log7 + log8 = log?
c. log_0.07(53) = log_10(53)/?
a. 1
b. 56
c. log_10(0.07)
400
How are exponential functions and logarithmic functions related?
They're inverses.
400
Use the definitions of sin and cos to write sin(theta) and cos(theta) for angles whose terminal side contains the given point.
(8,-3)
sin(theta) = -0.3511
cos(theta) = 0.9363
500
Find the particular equation of the exponential function.
y = 96*(0.5)^x
500
Find the indicated function value if f is a
a. Linear function
b. Power function
c. Exponential function
Given f(1)=1000 and f(3)=100, find f(9).
a. -2600
b. 10
c. 0.1
500
Solve the equation algebraically and check your solution.
ln (x+2) + ln(x-2) = 0
x = positive sqrt(5) since negative sqrt(5) leads to an undefined solution
500
How do you personally study for math tests?
Answers may vary.
500
If angle theta terminates in the third quadrant, what are the signs of the sin, cos, and radius?
Sin is negative, cos is negative, radius is positive (always!)