math section 1.2

A cell phone plan charges $30 per month for unlimited call and text messages, however each gigabyte (GB) of data is charged at a rate of $11 per GB. Assume that fractional values of a GB are prorated according to this rate. If a user uses more than 9 GB of data during their monthly billing cycle, then they are not charged more than the cost for the first 9 GB. Write a piecewise-defined function that describes the amount a cell phone user will pay, C, as a function of the number of GB of data they use, d, over the course of a month.

1. 11d+30 2. (brackets) 0,9 3. 129 4. (9, in) c(9)=11(9)+30=129

f g(x)=f(x+4)+3,

For example, the graph of the function f(x)=(x+4)2 is the graph of y=x2 shifted 4 units to the left. In another example, the graph of the function f(x)=(x−4)2 is the graph of y=x2 shifted 4 units to the right.For example, the graph of the function f(x)=x2+4 is the graph of y=x2 shifted up 4 units. In another example, the graph of the function f(x)=x2−4 is the graph of y=x2 shifted down 4 units.

For this problem, we need to recall that a piecewise function is defined by different formulas on different parts of its domain. Here, we see that since x=2 is greater than x=−4, it is in the domain of the second piece of the function. We will therefore evaluate f(2) by substituting x=2 into the second piece of the function. This piece has the algebraic form f(x)=(x+4)2−2.

f(2)=((2)+4)2−2=34

For this problem, we need to recall that a piecewise function is defined by different formulas on different parts of its domain. Here, we see that since x=4 is greater than x=0, it is in the domain of the second piece of the function. We will therefore evaluate f(4) by substituting x=4 into the second piece of the function. This piece has the algebraic form f(x)=−2x2.

f(4)=−2(4)2=−32

sketch graph

f(x)(5,1)(6,9)(7,10)(8,10)(10,2)→g(x)→(10,1/2)→(12,9/2)→(14,5)→(16,5)→(20,1) For example, the graph of the function f(x)=2x2 is the graph of y=x2 vertically stretched by a factor of 2. In another example, the graph of the function f(x)=12x2 is the graph of y=x2 vertically compressed by a factor of 2. For example, the graph of the function f(x)=(2x)2 is the graph of y=x2 compressed horizontally by a factor of 2. In another example, the graph of the function f(x)=(12x)2 is the graph of y=x2 stretched horizontally by a factor of 2.

f(x)={−x−1,x+1,x<−5x≥−5 Plot f(x) in the graphing window below. Drag the green movable dot across the top part of the graphing window to define the x-coordinate that limits the domain of each of the pieces of f(x). The pieces of the function are colored blue and red respectively. Then, adjust the "include"/"exclude" sliders to specify if an endpoint of an interval over which a piece is defined is open or closed. Notice that the endpoint will appear as a hollow circle if it's excluded from the domain of a piece, while a full circle if included.

green line 5, blue line excluded x=-5,4, red line included -5,4

The graph of f(x) is shown below as a red dashed curve. Drag the movable blue points to obtain the graph of g(x)=f(−x) , shown as a blue solid curve.

red (2,9),(3,5),(6,2),(7,4),(10,9) blue (-2,9),(-3,5),(-6.2),(-7,4), (-10,9)\ For example, the graph of the function f(x)=(−x)3 is the graph of y=x3 reflected about the y-axis. For example, the graph of the function f(x)=−x3 is the graph of y=x3 reflected about the x-axis.

A cell phone plan charges $20 per month for unlimited call and text messages, however each gigabyte (GB) of data is charged at a rate of $5 per GB. Assume that fractional values of a GB are prorated according to this rate. If a user uses more than 8 GB of data during their monthly billing cycle, then they are not charged more than the cost for the first 8 GB. Write a piecewise-defined function that describes the amount a cell phone user will pay, C, as a function of the number of GB of data they use, d, over the course of a month.

the first piece of C(d) is 5d+20, defined in the interval (brackets) (0,8). The second piece is 60, defined in the interval (8, in) 5x8+20=60.

A cell phone plan charges $20 per month for unlimited call and text messages, however each gigabyte (GB) of data is charged at a rate of $8 per GB. Assume that fractional values of a GB are prorated according to this rate. If a user uses more than 10 GB of data during their monthly billing cycle, then they are not charged more than the cost for the first 10 GB. Write a piecewise-defined function that describes the amount a cell phone user will pay, C , as a function of the number of GB of data they use, d , over the course of a month.

the first piece of C(d) is 8d+20, defined in the interval (0,10 brackets). the second piece is 100, defined in the interval (10,in)