1. ⓐ Evaluate p(−3).p(−3).
2. ⓑ Solve p(c)=2.
54. Given the following graph,
1. ⓐ Evaluate f(4).f(4).
2. ⓑ Solve for f(x)=1.f(x)=1.
Graph of relation.
For the following exercise, write an equation for the graphed function by using transformations of the graphs of one of the toolkit functions.
For the following exercise, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.
For the following exercise, solve the inequality and write the solution in interval notation.
64. The tolerance for a ball bearing is 0.01. If the true diameter of the bearing is to be 2.0 inches and the measured value of the diameter is xx inches, express the tolerance using absolute value notation.
find a domain on which this function f is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of f restricted to that domain.
Perform the indicated operation and express the result as a simplified complex number.
For the following exercise, use the vertex (h,k)(h,k) and a point on the graph (x,y)(x,y) to find the general form of the equation of the quadratic function.
For the following exercise, find the degree and leading coefficient for the given polynomial.
For the following exercise, determine the least possible degree of the polynomial function shown.
For the following exercise, graph the polynomial functions. Note x-x- and y-y- intercepts, multiplicity, and end behavior.
For the following exercise, use the graphs to write a polynomial function of least degree.
For the following exercise, use long division to divide. Specify the quotient and the remainder.
For the following exercise, use synthetic division to find the quotient and remainder.
For the following exercise, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.
For the following exercise, construct a polynomial function of least degree possible using the given information.
For the following exercise, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph.
For the following exercise, write an equation for a rational function with the given characteristics.
For the following exercise, find the inverse of the functions.
For the following exercise, find the inverse of the function and graph both the function and its inverse.
For the following exercise, consider this scenario: For each year t,t, the population of a forest of trees is represented by the function A(t)=115(1.025)t.A(t)=115(1.025)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t)=82(1.029)t.B(t)=82(1.029)t. (Round answers to the nearest whole number.)
For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.
ALGEBRAIC
For the following exercise, graph the transformation of f(x)=2x.f(x)=2x. Give the horizontal asymptote, the domain, and the range.
For the following exercise, rewrite each equation in exponential form.
Numeric
For the following exercise, evaluate the base b logarithmic expression without using a calculator.
For the following exercise, state the domain, range, and x- and y-intercepts, if they exist. If they do not exist, write DNE.
For the following exercise, sketch the graph of the indicated function.
For the following exercise, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.
For the following exercises, use logarithms to solve.
For the following exercise, use the one-to-one property of logarithms to solve.
Real-World Applications
For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour.
36. A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of carbon-14 is 57305730 years.)
Determine the domain of the functions below and write your answers in interval notation.
Determine the solutions to the inequalities below analytically and write your answers in interval notation.
In the following exercises, solve each rational inequality and write the solution in interval notation.
—
1. a Determine p(3). p(−3).
2. b Determine p(c)=2.
54. Given the graph below,
1. a Determine f(4).f (4).
2. b Determine f(x)=1.f(x)=1.
Relationship graph
For the next exercise, use transformations of the graphs of one of the toolkit functions to develop an equation for the graphed function.
Explain how the formula is a transformation of a toolkit function in the following exercise. Then, draw a transformation graph.
Solve the inequality and express the solution in interval notation for the following exercise.
A ball bearing has a tolerance of 0.01. If the true diameter of the bearing is to be 2.0 inches and the measured value of the diameter is xx inches, express the tolerance using absolute value notation.
find a domain on which this function
