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Write an equation of the line that passes through the given point and is perpendicular to the given line. Skill 7. Find an equation of the line through the points of intersection of and. Application The mathematical model for the data given below is where y represents the CPI and t represents the year, with corresponding to

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Simplify the result. Then simplify the expression. Evaluate the expression and then simplify the result. Find the domain and range of the function.

Evaluate the function at. Determine the domain and range of the function.

Determine whether y is a function of x. Use the graph of given below to find the graph of the function. Specify a sequence of transformations for the function that will yield the graph of h from the graph of the function.

The function is a horizontal shift to the right, followed by a vertical shift downwards. The function is a horizontal shift to the left, followed by a vertical shift upwards. The function is a horizontal shift to the left, followed by a horizontal shift to the right. The function is a vertical shift downwards, followed by a horizontal shift to the right.

The function is a vertical shift upwards, followed by a horizontal shift to the left. Given and , evaluate. Determine whether the function is even, odd, or neither. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even.

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. The horsepower H required to overcome wind drag on a certain automobile is approximated by where x is the speed of the car in miles per hour.

Round the numerical values in your answer to five decimal places.

An open box of maximum volume is to be made from a square piece of material centimeters on a side by cutting equal squares from the corners and turning up the sides see figure. Write the volume V as a function of x, the length of the corner squares.

What is the domain of the function. Evaluate a function and simplify MSC: Simplify a difference quotient MSC: Identify the domain and range of a function MSC: Evaluate a piecewise function MSC: Identify equations that are functions MSC: Graph transformations of functions MSC: Describe a transformation of an equation MSC: Evaluate composite functions MSC: Identify the type of symmetry of the graph of a function MSC: Identify points on a graph using symmetry MSC: Apply composite functions MSC: Create functions in applications MSC: Identify domains in applications MSC: Determine which type of function would be most appropriate to fit the given data.

Which function below would be most appropriate model for the given data? The following ordered pairs represent temperatures in degrees Fahrenheit taken each hour from 1: Let T be temperature, and let t be time, where corresponds to 1: Plot the data. Visually find a linear model for the data and find its equation. From the visual linear model that you created, determine which of the models that follow appears to best approximate the data.

Each ordered pair gives the exposure index x of a carcinogenic substance and the cancer mortality y per , people in the population. Use the model to approximate y if. Round your answer to one decimal place. Hooke's Law states that the force F required to compress or stretch a spring within its elastic limits is proportional to the distance d that the spring is compressed or stretched from its original length. That is, where k is a measure of the stiffness of the spring and is called the spring constant.

The table shows the elongation d in centimeters of a spring when a force of F newtons is applied. Use the regression capabilities of a graphing utility to find a linear model for the data.

Round the numerical values in your answer to three decimal places. Use a graphing utility to plot the data and graph the linear model. Use the model to estimate the elongation of the spring when a force of 55 newtons is applied.

Round your answer to two decimal places. In an experiment, students measured the speed s in meters per second of a falling object t seconds after it was released. The results are shown in the table below.

Round all numerical values in your answer to one decimal place. Use the model to estimate the speed of the object after seconds. Students in a lab measured the breaking strength S in pounds of wood 2 inches thick, x inches high, and 12 inches long.

Use the regression capabilities of a graphing utility to fit a quadratic model to the data. Use a graphing utility to plot the data and graph the quadratic model. Use the model to approximate the breaking strength when. A V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds x in thousands of revolutions per minute. Use the regression capabilities of a graphing utility to find a cubic model for the data.

Round the numerical values in your answer to three decimal places, where applicable. Use a graphing utility to plot the data and graph the cubic model. Use the model to approximate the horsepower when the engine is running at revolutions per minute.

Identify the most appropriate function for a scatter plot MSC: Identify the best linear model for given data MSC: Application 4. Evaluate linear models in applications MSC: Application 5.

Write a linear model for data using the regression capabilities of a graphing utility MSC: Application 6. Plot data points and the graph of a linear model MSC: Application 9. Plot data points and the graph of a quadratic model MSC: Evaluate quadratic models in applications MSC: Evaluate cubic models in applications MSC: Plot data points and the graph of a cubic model MSC: