Graph the following functions and describe how are they similar/different to the linear parent function \(f(x)=x\) (reference function).
1) \(g(x) = -x\)
2) \(h(x) = 2x + 4\)
3) \(k(x) = 13x\)
4) \(l(x) = x - 7\)
5) \(m(x) = -\Large\frac{2}{3}\normalsize x - 1\)
6) \(n(x) = 3x - 12\)
7) \(p(x) = -\Large\frac{4}{3}\normalsize x + 3\)
Write a function that fits the description below.
8) The function has a slope of two and is translated down by \(3\) units.
9) \(g(x)\) has a \(y\)-intercept of \(5\) and has a slope of \(-4\).
10) The function has been translated up by \(12\) units and has a decreasing slope of one-half.
11) The function is increasing faster than the reference function and has a y-intercept at the origin.
Given the following table, graph the function and describe how it compares to the linear parent function.
1) \(g(x) = -x\)
2) \(h(x) = 2x + 4\)
3) \(k(x) = 13x\)
4) \(l(x) = x - 7\)
5) \(m(x) = -\Large\frac{2}{3}\normalsize x - 1\)
6) \(n(x) = 3x - 12\)
7) \(p(x) = -\Large\frac{4}{3}\normalsize x + 3\)
Write a function that fits the description below.
8) The function has a slope of two and is translated down by \(3\) units.
9) \(g(x)\) has a \(y\)-intercept of \(5\) and has a slope of \(-4\).
10) The function has been translated up by \(12\) units and has a decreasing slope of one-half.
11) The function is increasing faster than the reference function and has a y-intercept at the origin.
Given the following table, graph the function and describe how it compares to the linear parent function.
12)
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13)
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Given the following graph describe how it relates to the linear parent function.
16) For the following two functions, \(g(x)\) and \(h(x)\), which function increases more rapidly?
Review
17) Complete the algebraic proof
17) Complete the algebraic proof
Statements |
Reasons |
\(-3(x + 4) = 5 - 8x + 4\) |
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\(-3(x + 4) = -8x + 9\) |
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\(-3x - 12 = -8x + 9\) |
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\(5x - 12 = 9\) |
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\(5x = 21\) |
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\(x = \dfrac{21}{5}\) |
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18) Complete the algebraic proof
Statements |
Reasons |
\(6(-2x + 1) = -\dfrac{3}{4}(x - 16)\) |
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\(-12x + 6 = -\dfrac{3}{4}(x - 16)\) |
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\(-12x + 6 = -\dfrac{3}{4}x + 12\) |
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\(-\dfrac{45}{4}x + 6 = 12\) |
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\(-\dfrac{45}{4}x = 6\) |
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\(x = -\dfrac{24}{45}\) |
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