Chapter 1.4 Practice

Questions

Question 1

  1. For each of these functions, determine the domain.
    1. \(f(x)=\frac{2x}{3x-1}\)
    2. \(f(x)=\frac{x}{x^2-1}\)
    3. \(f(x)=\frac{3}{x(x^2+1)}\)
    4. \(f(x)=4x+1\)
    5. \(f(x)=-4\)
    6. \(f(x)=\frac{x(x+1)(x-2)}{x(x+1)(x+2)}\)

Question 2

  1. Determine the slope and \(y\)-intercept on the line that is given below.
    1. \(f(x)=-4x+2\)
    2. \(f(x)=x-2\)
    3. \(f(x)=4\)
    4. \(f(x)=\frac{1}{2}x\)

Question 3

  1. Determine an equation for each line with the given properties
    1. The line with slope \(-\frac{1}{3}\) that passes through \((-4,3)\)
    2. The line with slope \(5\) with \(y\)-intercept \(-5\)
    3. The line with slope \(5\) with \(x\)-intercept \(-5\)
    4. The line that passes through the points \((-1,0)\) and \((3,11)\)

Question 4

  1. Determine an equation for a function \(f\) with these properties
    1. \(f\) is a monomial of degree 4 with coefficient equal to \(-2\)
    2. \(f\) is a monomial of degree 10 with coefficient equal to \(3\)
    3. \(f\) is a monomial of degree odd degree and coefficient equal to 1

Answers

Question 1

    1. \(\left(-\infty,\frac{1}{3}\right)\cup\left(\frac{1}{3},\infty\right)\)
    2. \(\left(-\infty,-1\right)\cup(-1,1)\cup\left(1,\infty\right)\)
    3. \((-\infty,0)\cup(0,\infty)\)
    4. \((-\infty,\infty)\)
    5. \((-\infty,\infty)\)
    6. \((-\infty,-2)\cup(-2,-1)\cup(-1,0)\cup(0,\infty)\)

Question 2

    1. slope is \(-4\), \(y\)-intercept is \(2\)
    2. slope is \(1\), \(y\)-intercept is \(-2\)
    3. slope is \(0\), \(y\)-intercept is \(4\)
    4. slope is \(\frac{1}{2}\), \(y\)-intercept is \(0\)

Question 3

    1. \(y=-\frac{1}{3}(x+4)+3\)
    2. \(y=5x-5\)
    3. \(y=5(x+5)\)
    4. \(y=\frac{11}{4}(x+1)\)

Question 4

    1. \(f(x)=-2x^4\)
    2. \(f(x)=3x^{10}\)
    3. \(f(x)=x\) or \(f(x)=x^3\) or \(f(x)=x^5\) or \(f(x)=x^7\) etc.

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