<h2>
Answer:</h2>
![\boxed{(-\infty,-3] \ U \ [3,4] \ U \ \{-2\}}](https://tex.z-dn.net/?f=%5Cboxed%7B%28-%5Cinfty%2C-3%5D%20%5C%20U%20%5C%20%5B3%2C4%5D%20%5C%20U%20%5C%20%5C%7B-2%5C%7D%7D)
<h2>
Step-by-step explanation:</h2>
To solve this problem we need to use the Test Intervals for Polynomial. The following steps helps us to determine the intervals on which the values of a polynomial are entirely negative or entirely positive.
1. Find all real zeros of the polynomial arranging them in increasing order from smallest to largest. We call these zeros the critical numbers of the polynomial.
Before we start applying this steps, let's multiply the entire inequality by -1 changing the direction of the inequality, so the result is:
So the real zeros are:
2. Use the real zeros of the polynomial to determine its test intervals.
3. Take one representative x-value in each test interval, then evaluate the polynomial at this value. If the value of the polynomial is negative, the polynomial will have negative values for every x-value in the interval. If the value of the polynomial is positive, the polynomial will have positive values for every x-value in the interval.
<u>Polynomial values</u>
___________________
___________________
At x = -3, x = 3, and x = 4 we use brackets because the inequality includes the value at which the polynomial equals zero.
Finally, if you set 
:
So is also a solution to the system. Finally, the solution is:
<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)
0 = ln (x - 4)
1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)
1 = ln (x - 4)
e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
*************************************************************************
transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>
Answer:
y - 9 = -14 (x + 2)
Step-by-step explanation:
Point-slope form --> y - y1 = m ( x - x1)
slope = -14
y1 = 9
x1 = -2
Let's put the values all together:
y - 9 = -14 (x - - 2)
y - 9 = -14 (x + 2) ---> final answer
Answer:
positive 9
Step-by-step explanation:
that's the answer
Answer: x=12
Step-by-step explanation: because I’m smart and in middle school
