When a function is shifted to the right by 1 unit it is moved towards the negative side so we would be adding -1 to the value of x. The function f(x) would be f(x-1). To determine the resulting function, we substitute to the parent function (x-1) to x. We do as follows:
<span>f (x) = x^3 + 2x^2 − 3x − 5
</span>f (x-1) = (x-1)^3 + 2(x-1)^2 − 3(x-1) − 5
f (x-1) = x^3 - 3x^2 + 3x - 1 + 2(x^2 - 2x + 1) - 3x + 3 - 5
f (x-1) = x^3 - 3x^2 + 2x^2 + 3x - 4x - 3x - 1 + 2 + 3 - 5
f (x-1) = <span>x^3 - x^2 - 4x - 1
Therefore, the correct answer is the last option.</span>
Answer:
4 1/2. Root 18 simplifies to 4.242640687, which is less than 4.50
B. 11.33 is closer to the area of a circle with a radius of 2.1
Answer:
!!!
Step-by-step explanation:
Answer:
Option B k > 0
Step-by-step explanation:
we know that
Observing the graph
The slope of the line is positive
The y-intercept is negative
we have
![3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)](https://tex.z-dn.net/?f=3y-2x%3Dk%285x-4%29%2B6%5C%5C%20%5C%5C3y%3D5kx-4k%2B6%2B2x%5C%5C%20%5C%5C3y%3D%5B5k%2B2%5Dx%2B%286-4k%29%5C%5C%20%5C%5Cy%3D%5Cfrac%7B1%7D%7B3%7D%5B5k%2B2%5Dx%2B%282-%5Cfrac%7B4%7D%7B3%7Dk%29)
The slope of the line is equal to
![m=\frac{1}{3}[5k+2]](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D%5B5k%2B2%5D)
Remember that the slope must be positive
so
The value of k is greater than -2/5
Analyze the y-intercept
1.5 is greater than zero
so
the solution for k is the interval ------> (1.5,∞)
therefore
must be true
k > 0
