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kumpel [21]
2 years ago
9

Let g(x) be the reflection of f(x) = 3x + 2 in the x-axis. What is a function rule for g(x)?

Mathematics
1 answer:
BartSMP [9]2 years ago
7 0

The reflection of f(x) = 3\cdot x + 2 in the x-axis is g(x) = -3\cdot x - 2. The function used to derive g(x) is: g(x) = -f(x). (Correct choice: g(x) = -3\cdot x - 2)

Mathematically speaking, a reflection in the x-axis is defined by the following expression:

g(x) = -f(x) (1)

Where:

  • f(x) - Original function.
  • g(x) - Reflected function.

If we know that f(x) = 3\cdot x + 2, then the expression for g(x) is:

g(x) = - (3\cdot x + 2)

g(x) = -3\cdot x - 2

The reflection of f(x) = 3\cdot x + 2 in the x-axis is g(x) = -3\cdot x - 2. The function used to derive g(x) is: g(x) = -f(x).

We kindly invite to see this question on reflections: brainly.com/question/23558898

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Given h(x) = -5x + 3, find h(5).
lyudmila [28]
5x+5=3
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6 0
3 years ago
Determine the range of the function graphed above.
Sever21 [200]

Answer:

D. (-∞,4]

Step-by-step explanation:

The range is the y values

The lowest y values is negative infinity

The highest y values is 4

( - inf, 4]

We use the parentheses since we cannot get to negative infinity, the bracket since we reach 4

8 0
3 years ago
The line through (-1/2, -7/2) and (2, 14) in slope intercept form??
icang [17]
To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope (m):

m =  \frac{y_{2}-y _{1}}{x_{2}-x_{1}}

We can replace the variables in this equation with the values from the points we have been given, (\frac{-1}{2},  \frac{-7}{2}) and (2, 14). We know that the x-values always come first in an ordered pair, so we can put those in our equation first.
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair x_{2} and the \frac{-1}{2} in the first ordered pair x_{1}.
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.

m =  \frac{y_{2}-y _{1}}{x_{2}-x_{1}}

m =  \frac{14 -  \frac{-7}{2} }{2 -  \frac{-1}{2} }

Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as

m =  \frac{14 +  \frac{7}{2} }{2 +  \frac{1}{2} }

and we can change the improper fraction in the numerator into a mixed number for ease of addition.

m =  \frac{14 + 3 \frac{1}{2} }{2+ \frac{1}{2} }

And here, we can add, since it's made simple for us.

m =  \frac{17  \frac{1}{2} }{2  \frac{1}{2} }

Finally, to get the slope we can complete the fraction by dividing.

17.5 ÷ 2.5 = 7

The slope of this equation, m, is 7, and so far, our equation looks like this:

y = 7m + b

Now, to find y-intercept.

To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.

y = 7x + b

Let us substitute in our values.

14=7(2)+b

Now, we can solve by multiplying the 7 and 2.

14=14+b

Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with

0 = b

which can be flipped around to show

b=0

The y-intercept of this line is 0.

Now, we can make this known in our equation like this:

y=7x+0

Or, for neatness' sake, we can just say

y=7x

which is your final equation.

The line through (\frac{-1}{2},  \frac{-7}{2}) and (2, 14) in slope-intercept form is <span>y=7x.
Hope that helped! =) </span>


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Answer:

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Step-by-step explanation:

Do it yourself

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