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Mnenie [13.5K]
3 years ago
14

How do you find the domain on this type of graph

Mathematics
1 answer:
xz_007 [3.2K]3 years ago
5 0

Answers:

Domain:  x \ge -5

Range:  y \ge -2

========================================

Explanation:

The domain is the set of all allowed x values of a function. The point on the very left shows that x = -5 is the smallest value possible. So this means the domain consists of x values such that x = -5 or x > -5. We shorten that to x \ge -5

------------------

The range is the set of possible y outputs. The lowest point is when y = -2 meaning that y \ge -2 is the range (so y can be -2 or larger).

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Let <em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² + <em>cx</em> + <em>d</em>.

The graph of <em>f(x)</em> passes through (4, -22) and (3, -26), which means <em>f</em> (4) = -22 and <em>f</em> (3) = -26, so that

64<em>a</em> + 16<em>b</em> + 4<em>c</em> + <em>d</em> = -22

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When the question says it has tangents at some point, I take that to mean the slope of the tangent line at that point is the given number. So <em>f '</em> (4) = 11 and <em>f '</em> (3) = -2. We have

<em>f '(x)</em> = 3<em>ax</em> ²+ 2<em>bx</em> + <em>c</em>

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48<em>a </em>+ 8<em>b </em>+ <em>c</em> = 11

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Solve the system:

• Eliminate <em>d</em> :

(64<em>a</em> + 16<em>b</em> + 4<em>c</em> + <em>d</em>) - (27<em>a</em> + 9<em>b</em> + 3<em>c</em> + <em>d</em>) = -22 - (-26)

→   37<em>a</em> + 7<em>b</em> + <em>c</em> = 4

• Eliminate <em>c</em> :

(48<em>a </em>+ 8<em>b </em>+ <em>c</em>) - (27<em>a </em>+ 6<em>b</em> + <em>c</em>) = 11 - (-2)

→   21<em>a</em> + 2<em>b</em> = 13

(48<em>a </em>+ 8<em>b </em>+ <em>c</em>) - (37<em>a</em> + 7<em>b</em> + <em>c</em>) = 11 - 4

→   11<em>a</em> + <em>b</em> = 7

• Eliminate <em>b</em>, then solve for <em>a</em> and the other variables:

(21<em>a</em> + 2<em>b</em>) - 2 (11<em>a</em> + <em>b</em>) = 13 - 2 (7)

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Then

<em>f(x)</em> = <em>x</em> ³ - 4<em>x</em> ² - 5<em>x</em> - 2

7 0
4 years ago
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