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Home Question Bank Math Pre Calculus Archive 2025 January 10

Pre-calculus Questions from Jan 10,2025

Browse the Pre-calculus Q&A Archive for Jan 10,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Let \( f(x)=\frac{1}{x} \) Write a formula for a function \( g \) whose graph is obtained from the graph of \( f(x) \) after the following sequence of transformations: (1) scale vertically by a factor of 5 ; (2) shift left 5 unit (3) shift up 3 units. \( g(x)= \) Let \( f(x)=\sqrt{x} \) If \( g(x) \) is the graph of \( f(x) \) reflected across the \( x \)-axis and then shifted down 2 units, write a formula for \( g(x) \). \( g(x)=\square \) Enter \( \sqrt{x} \) as \( \operatorname{sgrt}(\mathrm{x}) \). Graph the rational function. \[ f(x)=\frac{4 x-6}{-x+2} \] start by drawing the vertical and horizontal asympitotes Consider the function \( f(x) = \sqrt{x} \). Describe how you would graph its inverse, and explain any transformations that occur. In 1990, Nigeria had a population of about 95.3 million. E there were about 122.4 million people, an increase of about \( 28.4 \% \). During that decade, the population can be reasonably modeled by an exponential function. 1. Express the population of Nigeria, \( f(x) \) in millions of people, decades since 1990 . In 1990, Nigeria had a population of about 95.3 million. By 2000 , there were about 122.4 million people, an increase of about \( 28.4 \% \). During that decade, the population can be reasonably modeled by an exponential function. 1. Express the population of Nigeria , \( f(x) \) in millions of people, decades since 1990 . Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{2-1}+1 \). Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: \( \begin{array}{lll}3.1 & \text { Shift two units to the left } \\ 3.2 & \text { Shift } 3 \text { units up } \\ 3.3 & \text { Shift } 1 \text { unit right and } 2 \text { units down } \\ 3.4 & \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1\end{array} \) 1.2 If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real. 1.2.3 \( \quad f(x) \) undefined 1.2.4 \( f(x)>0 \) If the function \( g(x) = x^{2} + 5 \) has an inverse, determine the domain of the inverse function.
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