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Home Question Bank Math Pre Calculus Archive 2024 December 09

Pre-calculus Questions from Dec 09,2024

Browse the Pre-calculus Q&A Archive for Dec 09,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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QUESTION 4 Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). Explain how to use the end behavior of the function \( f(x)=\frac{x^{2}-6}{4 x^{2}-3 x-1} \) to determine the horizontal asymptote of the graph. Then explain why using end behavior for finding the horizontal asymptote works the same as using the ratio of the leading terms. Substituting increasingly by using the ratio of the leading terms because the numerator and the denominator are each polynomials whose end behavior is determined by their leading terms. Since the degree of the numerator is the degree of the denominator, the Which line is a common asymptote among the graphs of all of the functions below? \( f(x)=\frac{11}{x^{2}-9}-9 \quad g(x)=\frac{22}{x^{2}-4 x+3}-3 \) \( h(x)=\frac{8}{x^{2}-x-6} \) A \( x(x)=\frac{9}{x^{2}+2 x-15} \) A. \( x=3 \) B. \( x=-3 \) C. \( x=5 \) D. \( x=-4 \) E. \( x=-5 \) Which grows faster over time: \( y=2 x+1 \) or \( y=2^{x} ? \) a. both grow at the same rate While hiking, Marek throws a rock off a diff that is roughly 10 meters above a lake. This situation is modeled by the equation \( h=-4.9 t^{2}+10 \), with \( h \) representing the height in meters and \( t \) the time in seconds. If you were to set up a table to determine when the rock hits the water, what would be a reasonable scale for the range? ( 1 point) \( \frac{1}{10} \) 2 5 10 A volleyball is served by a 6 -foot player at an initial upward velocity of 33 feet per second The situation is modeled by the equation \( h=-16 t^{2}+33 t+6 h \) representing the height in feet and \( t \) representing the time in seconds. Using this equation, define the domain of the ball when it reaches its maximum height. ( 1 point) -1.03 seconds 1.03 seconds 23.01 feet - 1.22 seconds 14. Given the equation of the hyperbola bellow, find the vertices and foci. please write gour ansivers as ordered pairs, and leave any square roots in the answer, do not give any answers as a decimal. \( \frac{y^{2}}{25}-\frac{x^{2}}{16}=1 \) he graph of \( y=-3 x^{2} \) shifted 2 units above the origin. A tourist visiting New York City (unwisely) throws a penny off the top of a skyscraper. The height of the penny, \( h \) (in feet), \( t \) seconds after he throws it is modeled by the function \( h(t)=-16 t^{2}+20 t+759 \). How many seconds does it take for the penny to hit the ground? (Luckily it doesn't hit anyone!) Enter an exact expression, or round your answer to the nearest thousandth. A football player kicks the ball with an initial upward velocity of 60 feet per second This siluation is modeled using the equation \( h=-16 t^{2}+60 t+0 \), where \( h \) is the hoight in feet and \( t \) is the time in seconds. Using this equation, what is the maximum range the ball will reach? Round to the nearest hundredth. (1 point)
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