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Home Question Bank Math Pre Calculus Archive 2024 November 05

Pre-calculus Questions from Nov 05,2024

Browse the Pre-calculus Q&A Archive for Nov 05,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Suppose the graph of \( f \) is given. To obtain the graph of \( y=f(x-5) \), we must shift the graph of \( f(x) \) Evaluating an exponential function that models a real-wortd situation If the rate of inflation is \( 2.6 \% \) per year, the future price \( p(t) \) (in dollars) of a certain item can be modeled by the following exponential function, where \( t \) is the number of years from today. Find the current price of the item and the price 9 years from today. Round your answers to the nearest dollar as necessary. Current price: Price 9 years from today: Express the function in the form \( f \circ g \). \( H(x)=\sqrt{4+\sqrt{x}} \) a. \( f(x)=\sqrt{x}, g(x)=\sqrt{4+x} \) b. \( f(x)=\sqrt{4+x}, g(x)=\sqrt{x} \) c. \( f(x)=\sqrt{4-x}, g(x)=x^{2} \) d. \( f(x)=\sqrt{x}, g(x)=\sqrt{4-x} \) e. \( f(x)=\sqrt{x-4}, g(x)=\sqrt{x} \) Explain how the graph of \( g \) is obtained from the graph of \( f \). \( f(x)=\sqrt{x}, g(x)=\frac{1}{2} \sqrt{x-5} \) a. The graph of \( g(x)=\frac{1}{2} \sqrt{x-5} \) is obtained by shifting the graph of \( f(x)=\sqrt{x} \) upward 5 units, and then shrinking the graph vertically by a factor of \( \frac{1}{2} \). b. The graph of \( g(x)=\frac{1}{2} \sqrt{x-5} \) is obtained by shifting the graph of \( f(x)=\sqrt{x} \) to the left 5 units, and then shrinking the graph vertically by a factor of \( \frac{1}{2} \). che graph of \( g(x)=\frac{1}{2} \sqrt{x-5} \) is obtained by shifting the graph of \( f(x)=\sqrt{x} \) to the right 5 units. The graph of \( g(x)=\frac{1}{2} \sqrt{x-5} \) is obtained by shifting the graph of \( f(x)=\sqrt{x} \) downward 5 units. The graph of \( g(x)=\frac{1}{2} \sqrt{x-5} \) is obtained by shifting the graph of \( f(x)=\sqrt{x} \) to the right 5 units, and then shrinking the graph vertically by a factor of \( \frac{1}{2} \). e. the Suppose the graph of \( f \) is given. Describe how the graph of the function can be obtained from the graph of \( f \). \( y=7 f(x)-3 \) a. Stretch the graph of \( y=f(x) \) vertically by a factor of 3 , and then shift downward 7 units. b. Reflect the graph of \( y=f(x) \) about the \( y \)-axis, and then shift downward 3 units. c. Stretch the graph of \( y=f(x) \) vertically by a factor of 7 , and then shift downward 3 units. d. Stretch the graph of \( y=f(x) \) vertically by a factor of 7 , and then shift upward 3 units. e. Stretch the graph of \( y=f(x) \) vertically by a factor of 3 , and then shift upward 7 units. Suppose the graph of \( f \) is given. Describe how the graph of the function can be obtained from the graph of \( f \). \( y=f(-x) \) a. Reflect the graph of \( y=f(x) \) about the \( x \)-axis and stretch vertically by a factor of 6 . b. Reflect the graph of \( y=f(x) \) about the \( y \)-axis, c. Reflect the graph of \( y=f(x) \) about the \( x \)-axis. d. Reflect the graph of \( y=f(x) \) about the \( x \)-axis, and then shift upward 3 units. e. Reflect the graph of \( y=f(x) \) about the \( y \)-axis and stretch vertically by a factor of 3 . Find a Cartesian equation for the curve. \[ r=5 \cos (\theta) \] \( \square \) Consider the following curve. \[ r^{2} \cos (2 \theta)=25 \] Write an equation for the curve in terms of \( \sin (\theta) \) and \( \cos (\theta) \) Consider the following curve. \[ r^{2} \cos (2 \theta)=25 \] Write an equation for the curve in terms of \( \sin (\theta) \) and \( \cos (\theta) \) Find a Cartesian equation for the curve. Find a polar equation for the curve represented by the given Cartesian equation. (Assume \( 0 \leq \theta<2 \pi \).) \[ x=-8 \] Need Help? Read It
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