Which graph represents the same relation as the rule y = 2x, for all real numbers x?
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Given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and by substituting their values into f(x) = 3x + 6. We will have the following:
<em><u>Given:</u></em>
- f(x) = 3x + 6
<em>We are told to find:</em>
- f(a)
- f(a + h), and
1. <em><u>Find f(a):</u></em>
- Substitute x = a into f(x) = 3x + 6
f(a) = 3(a) + 6
f(a) = 3a + 6
<em>2. Find f(a + h):</em>
- Substitute x = a + h into f(x) = 3x + 6
f(a + h) = 3(a + h) + 6
f(a + h) = 3a + 3h + 6
<em>3. Find </em><em>:</em>
- Plug in the values of f(a + h) and f(a) into
Thus:
- Add like terms
Therefore, given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and by substituting their values into f(x) = 3x + 6. We will have the following:
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