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Questions and Answers
What is the domain of the function f(x) = |x - 5|?
What is the domain of the function f(x) = |x - 5|?
- (-5, ∞)
- [0, ∞)
- (-∞, ∞) (correct)
- (-5, 5)
What is the graph of the function g(x) = -x + 2 + 1?
What is the graph of the function g(x) = -x + 2 + 1?
- Graph B
- Graph C
- Graph D
- Graph A (correct)
Which of the following functions has an inverse function?
Which of the following functions has an inverse function?
- Graph B
- Graph C (correct)
- Graph A
- Graph D
What is the value of x that satisfies the equation 3^4x - 1 = 6?
What is the value of x that satisfies the equation 3^4x - 1 = 6?
What is the solution to the inequality -2 < 21 - 2y < 10?
What is the solution to the inequality -2 < 21 - 2y < 10?
What is the domain of the function f(x) = 3 - x?
What is the domain of the function f(x) = 3 - x?
What is the value of ln e^(6/5)?
What is the value of ln e^(6/5)?
What is the solution to the equation |3x - 2| = 5?
What is the solution to the equation |3x - 2| = 5?
What is the value of x in the solution to the system of equations 3x - y = 5 and 2x + 3y = -4?
What is the value of x in the solution to the system of equations 3x - y = 5 and 2x + 3y = -4?
What type of symmetry does the graph of 7y^2 = 4x^3 - 5 possess?
What type of symmetry does the graph of 7y^2 = 4x^3 - 5 possess?
What is the equation that can be used to determine how long it will take a $1000 investment to double if it is invested at 6% interest compounded continuously?
What is the equation that can be used to determine how long it will take a $1000 investment to double if it is invested at 6% interest compounded continuously?
What is the accumulated value of an investment of $5000 after 10 years at an interest rate of 6.3% if the interest is compounded continuously?
What is the accumulated value of an investment of $5000 after 10 years at an interest rate of 6.3% if the interest is compounded continuously?
Which of the following is the correct graph of the function f(x) = log2(x-1)?
Which of the following is the correct graph of the function f(x) = log2(x-1)?
What is the value of the expression log7(59) in terms of a and b?
What is the value of the expression log7(59) in terms of a and b?
What is the inverse of the function f(x) = 2x - 3?
What is the inverse of the function f(x) = 2x - 3?
What is the value of the expression f(x + h) - f(x) / h when f(x) = 2x^2 - 2x + 1?
What is the value of the expression f(x + h) - f(x) / h when f(x) = 2x^2 - 2x + 1?
What is the solution to the equation 3ln(4x) = 6?
What is the solution to the equation 3ln(4x) = 6?
What are the x-intercepts of the graph of the function f(x) = 3x^2 - 2x + 1?
What are the x-intercepts of the graph of the function f(x) = 3x^2 - 2x + 1?
What is the value of log3(81x2) in terms of log3x?
What is the value of log3(81x2) in terms of log3x?
What is the value of logb(y - 4x - z) in terms of logb(y), logb(x), and logb(z)?
What is the value of logb(y - 4x - z) in terms of logb(y), logb(x), and logb(z)?
What is the value of (gf)(4) if f(x) = logb(x) and g(x) = x + 12?
What is the value of (gf)(4) if f(x) = logb(x) and g(x) = x + 12?
What is the graph of the function f(x) = 2^{-x}?
What is the graph of the function f(x) = 2^{-x}?
What is the value of f(-1) if f(x) = 2x + 3 for x ≤ -1 and f(x) = 1 - 5x for x > -1?
What is the value of f(-1) if f(x) = 2x + 3 for x ≤ -1 and f(x) = 1 - 5x for x > -1?
What is the equation of the asymptote for the graph of f(x) = 2x + 3?
What is the equation of the asymptote for the graph of f(x) = 2x + 3?
What is the quadratic equation that needs to be solved in the process of solving the radical equation x − 5 = 3x − 11?
What is the quadratic equation that needs to be solved in the process of solving the radical equation x − 5 = 3x − 11?
Which of the following relations defines y as a function of x?
Which of the following relations defines y as a function of x?
What is the distance between the points (5, 4) and (1, -1)?
What is the distance between the points (5, 4) and (1, -1)?
What is the symmetry of the graph shown below, and what type of function does it represent?
What is the symmetry of the graph shown below, and what type of function does it represent?
What is the revenue generated by selling 10 items, according to the function p(x) = -x² + 26x + 300?
What is the revenue generated by selling 10 items, according to the function p(x) = -x² + 26x + 300?
What is the maximum revenue that the company may achieve for sales of the item, according to the function p(x) = -x² + 26x + 300?
What is the maximum revenue that the company may achieve for sales of the item, according to the function p(x) = -x² + 26x + 300?
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Study Notes
Logarithms and Exponents
log3 ( 81x 2 )can be expressed in different ways:log3 ( 81 ) + 2log3 x,4 + 2log3 x,log3 ( 81 ) - 2log3 x,log3 ( 81/x 2 ), or4log3 x- The formula
logb y - logb x - logb zis equal tologb (y/xz) f(x) = 2^(-x)andg(x) = xhave a composite function(gf)(x)
Graphs and Functions
f(x) = 2^(-x)has a graph that is a reflection ofy = 2^xacross the y-axisf(x) = x^2 + 4is an even function, meaningf(-x) = f(x)f(x) = x^3 + 4xis an odd function, meaningf(-x) = -f(x)y = f(x) - 3has a graph that is a vertical translation ofy = f(x)down 3 units
Exponential Equations
ln(5t + 1) - ln(t + 2) = ln 3can be solved by using the properties of logarithmslog x + log(2x + 1) = 1can be solved by using the properties of logarithms2^(x-2) - 3 = 0can be solved by using the properties of exponents
Inequalities
2x - 5 < 3can be solved by adding 5 to both sides and then dividing both sides by 2-2 < 21 - 2y < 10can be solved by adding 2y to all parts of the inequality and then dividing all parts by 2
Systems of Equations
3x - y = 5and2x + 3y = -4can be solved by using substitution or elimination methods
Compound Interest
- The formula
A = Pe^(rt)can be used to calculate the accumulated value of an investment, whereAis the accumulated value,Pis the principal,ris the interest rate, andtis the time in years - The formula
A = P(1 + r/n)^(nt)can be used to calculate the accumulated value of an investment with compound interest, whereAis the accumulated value,Pis the principal,ris the interest rate,nis the number of times interest is compounded per year, andtis the time in years
Symmetry and Graphs
- A graph is symmetric with respect to the x-axis if
f(-x) = f(x) - A graph is symmetric with respect to the y-axis if
f(x) = f(-x) - A graph is symmetric with respect to the origin if
f(-x) = -f(x) - A function is even if
f(-x) = f(x)and odd iff(-x) = -f(x)
Distance and Midpoint
- The distance between two points
(x1, y1)and(x2, y2)can be calculated using the formulad = sqrt((x2 - x1)^2 + (y2 - y1)^2) - The midpoint of a line segment with endpoints
(x1, y1)and(x2, y2)can be calculated using the formula((x1 + x2)/2, (y1 + y2)/2)
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