College Algebra

1. For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin?(No explanation required. Just answer Yes or No to each question.)

(a) Symmetric with respect to the x-axis? ____ y-axis? ____ origin? ____

(b) Symmetric with respect to the x-axis? ____ y-axis? ____ origin? ____

2. Let . (no explanation required)

(a) State the zero(s) of the function. ________

(b) Which of the following is true? 2. ______

A. f is an even function.

B. f is an odd function.

C. f is both even and odd.

D. f is neither even nor odd.

3. Which of the following equations does the graph represent? Show work or explanation. 3. ______

A. B. C. D.

4. Consider the points (–5, –2) and (–1, 4).

(a) Find the slope-intercept equation of the line passing through the two given points. Show work.

(b) Graph the line you found in (a), either drawing it on the grid in the previous problem #3, or generating the graph electronically and attaching it.

(c) Compare your line for this problem, #4, with the line in the previous problem #3. Are the two lines parallel, perpendicular, or neither parallel nor perpendicular? (The terms parallel and perpendicular are discussed on pages 166 and 167.) No explanation required – just state the answer.

5.

The amount of home heating oil h in gallons in a tank t days after a fill-up is modeled by

h(t) = –0.08t2 – 3t + 275 for 0 t 10.

Find and interpret the average rate of change of h over the interval [0, 10]. Show work.

6. Mike wants to purchase custom-made pens to advertise his business. Two companies offer different deals:

Company A: Pay a design fee of $27.00, plus $0.18 per pen

or Company B: Pay a design fee of $15.00, plus $0.24 per pen

(a) State a linear function f (x) that represents Company A's total charge for an order of x pens.

(b) State a linear function g(x) that represents Company B's total charge for an order of x pens.

(c) Mike wants to purchase 140 custom-made pens, as cheaply as possible. With which company should he place his order? Show work/explanation.

(d) For what number of pens is the total charge exactly the same for both companies? Show algebraic work/explanation.

(e) Fill in the blanks:

Company A is the cheaper option if ________(choose less or more ) than ______ (enter number) pens are ordered.

7. A graph of y = f (x) follows. No formula for f is given. 7. _______

Which graph (A, B, C, or D) represents the graph of y = f (x + 1) 2 ?

BRIEFLY EXPLAIN how you have decided which graph is the correct one.

(Grid supplied for scratch work; You are NOT required to submit your own graph)

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y = f(x)

A. (below) B. (below)

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C. (below) D. (below)

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8. ( no explanation required)

Consider the graph of the piecewise function y = f (x) pictured below.

(a) State the value of f (3).

(b) State the x-intercept(s), if any.

(c) State the y-intercept(s), if any.

(d) State the domain of the piecewise function.

(e) State the range of the piecewise function.

(f) State the interval(s) on which the function is increasing. That is, for what x-values is the function increasing?

(g) State the interval(s) on which the function is decreasing. That is, for what x-values is the function decreasing?

9. Based on data retrieved from http://www.erh.noaa.gov/lwx/climate/dca/dcatemps.txt the following chart of Washington, DC yearly average temperatures has been prepared.

The line of best fit, the regression line, is y = 0.0344x – 10.107, where x = year and y = average Washington, DC temperature, in degrees. The value of r2 is 0.6242.

(a) Use the regression line to estimate the average Washington, DC temperature in 1890, to the nearest tenth of a degree. Show some work.

(b) Use the regression line to predict the average Washington, DC temperature in 2018, to the nearest tenth of a degree. Show some work.

(c) In what year (to the nearest year) does the regression line predict an average Washington, DC temperature of 62.0 degrees? Show work, solving an appropriate equation.

(d) What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what the slope is telling us, in the context of this real-world application.

(e) What is the value of the correlation coefficient, r ? Also, interpret its value: Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?

10. Find all real solutions. Show work

-1

Washington DC Avg Temp

Avg Temp 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 54.8 54.8 54.8 56 52.2 54.3 55.5 56 55.8 55.6 56 54.9 54 55.1 53 53.4 54.8 53.6 55.1 56.3 55.4 54 53.7 56.4 54.2 55.5 54.9 56.1 54.4 56.5 54.1 54.8 54.3 52.2 54.1 55.9 53.5 55.4 55.2 55.2 56.4 54.5 57.3 54.9 55.6 55 53 55.6 56.4 54.7 58 56.4 56.1 54.1 56.1 54.5 56.3 56 56.5 57.5 58.2 57.3 57.1 55.9 55.8 56.3 56.4 57.6 57.8 54.8 57.6 57.2 56.9 56.9 57.1 58 56.5 56.6 59 56.9 57.6 57.6 58.9 57.7 57.1 56.3 58 55.5 58.9 56.3 56.7 55.8 55.7 57.5 56.8 56.8 56.4 57.5 57.2 57.7 57.9 56.7 59.3 58.8 59.4 57.9 58.6 58.1 58.1 59.5 59 57.7 58.4 57.8 58.2 57.8 58.1 57.1 56.9 60 60.2 56.7 57.7 58.3 57.9 56.9 58 60 58.9 57 58.5 59.3 56.4 58 59 59.1 59 59.2 57.4 59.8 59.9 61.5

Year

Average Temperature (degrees)