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Dmitry_Shevchenko [17]

3 years ago

7

For the functions f(x) = 2x + 3 and g(x) = 6x + 2, which composition produces the greatest output?

1 answer:

UkoKoshka [18]3 years ago

8 0

Given:
f(x) = 2x + 3
g(x) = 6x + 2

Therefore
(f.g)(x) = 2(6x+2) + 3 = 12x + 7
This is a straight line with slope = 12, and y-intercept = 7.

(g.f)(x) = 6(2x+3) + 2 = 12x + 20
This is a straight line with slope = 12 and y-intercept = 20.

The two compositions represent straight lines with a slope of 12.
Because (g.f)(x) has a higher intercept, it produces the greatest output.

Answer:
g(f(x)) produces the greatest output.

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4 years ago

Which equation has a graph that passes through the points at (0,5) and (-3,-4)?

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Answer:

$y = 3x + 5$

Step-by-step explanation:

We are asked the equation of the graph which passes through the points at (0,5) and (-3,-4).

Now, we know that the equation of a straight line passing through the points ( $x_{1},y_{1}$ ) and ( $x_{2},y_{2}$ ) is given by

$\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}$ .

So, in our case ( $x_{1},y_{1}$ ) ≡ (0,5) and ( $x_{2},y_{2}$ ) ≡ (-3,-4)

Therefore, the equation of the straight line will be

$\frac{y - 5}{5 - (- 4)} = \frac{x - 0}{0 - (- 3)}$

⇒ $y - 5 = \frac{9}{3}x$

⇒ $y = 3x + 5$ (Answer)

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4 years ago