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Home Question Bank Math Pre Calculus Archive 2025 January 23

Pre-calculus Questions from Jan 23,2025

Browse the Pre-calculus Q&A Archive for Jan 23,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Analyze the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[-3]{x} \) when \( f(x) \) is replaced by \( f(b x) \) and \( b \) is greater than 1. (1 point) The \( y \)-intercept does not change. The \( y \)-intercept shifts up by a distance of \( b \). The \( y \)-intercept stretches horizontally by a factor of \( b \). The \( y \)-intercept compresses horizontally by a factor of \( b \). Analyze the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by af \( (x) \) and a is positive. (1 point) The \( y \)-intercept shifts to the left by a distance of \( a \). The \( y \)-intercept does not change. The \( y \)-intercept shifts up by a distance of \( a \). The \( y \)-intercept shifts down by a distance of \( a \). True or False? Given the graph of the function \( f(x)=\sqrt[3]{x} \), when horizontally stretched, the new function domain and range will change. Option \#1: True Option \#2: False (1 point) The best answer is Option \# . How much would you have to deposit in an account with a \( 5 \% \) interest rate, compounded annually, to have \( \$ 1300 \) in your account 13 years later? \[ P=\$[?] \] \( F=P\left(1+\frac{1}{n}\right)^{\text {nt }} \) Given the function \( f(x)=\sqrt[3]{x} \), what is the new function after a horizontal stretch by a factor of 4? Option \#1: \( f(x)=\sqrt[3]{4 x} \) Option \#2: \( f(x)=4 \sqrt[3]{x} \) Option \#3: \( f(x)=\sqrt[3]{0.25 x} \) Option \#4: \( f(x)=0.25 \sqrt[3]{x} \) For each year, \( t \), the population of a forest of trees, call it Forest \( A \), is represented by the function \( A(t)=111(1.025)^{t} \). In a neighboring forest, call it Forest \( B \), the population of the same type of tree is represented by the function \( B(t)=82(1.03)^{t} \). \( a \). Which forest's population is growing at a faster rate? Select an answer \( \hat{v} \) \( b \). Which forest had a greater number of trees initially? Select an answer \( \hat{v} \) By how many (round to the nearest tree)? trees \( c \). Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 50 years (round to the nearest tree)? Select an answer \( \hat{v} \) By how many? Given the function \( f(x)=\sqrt[3]{x} \), what is the new function when \( f(x) \) is shifted 7 units to the right? Option \#1: \( f(x-7)=\sqrt[3]{x-7} \) Option \#2: \( f(x+7)=\sqrt[3]{x+7} \) Option \#3: \( f(x)+7=\sqrt[3]{x}+7 \) Option \#4: \( f(x)+7=\sqrt[3]{x}-7 \) (1 point) The best answer is Option \# Analyze the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is reptaced by \( f(x)+d \) and \( d \) is positive. (1 point) The \( y \)-intercept shifts up by a distance of \( d \). The \( y \)-intercept shifts to the right by a distance of \( d \). The \( y \)-intercept shifts to the left by a distance of \( d \). The \( y \)-intercept shifts down by a distance of \( d \). What is the range of \( f(x)=\sqrt[3]{x-4} \) ? (1 point) \( \{y|y \in \mathbb{R}|\} \) \( \{x \mid-\infty<x<\infty\} \) \( \{y|0<y<\infty|\} \) \( \{x \mid-\infty \leq x \leq \infty\} \) What is the domain of \( g(x)=-\sqrt[3]{x}+5 \) ? (1 point) \( -\infty<x<\infty \) \( 0<x<\infty \) \( 0 \leq y \leq \infty \) \( -\infty \leq y \leq \infty \)
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