Answer:
A graph showing a range of negative three to two on the x and y axes. A dotted line with arrows at both ends that passes through the x axis at two and runs parallel to the y axis. The graph is shaded to the left of the line.
Step-by-step explanation:
The inequality given is x < 2. This means x is less than two are the values that satisfy the equation.
The equation can be written as x=2 to identify the position where the line will pass. The line is dotted and will pass through x=2 to be parallel with the y-axis.
The second and third answers are not correct because the line should not be solid.
The first answer is not correct because the shaded part should be to the left of the line.
Answer:
Step-by-step explanation:
If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away. If there is, this affects the domain. The domain are the values in the denominator that the function covers as far as the x-values go. If we factor both the numerator and denominator, we get this:
Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away. That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x. The other factor, (x - 4), does not cancel out. This is called a vertical asymptote and affects the domain of the function. Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4. That means that the function has to split at that x-value. It comes in from the left, from negative infinity and goes down to negative infinity at x = 4. Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity. The domain is:
(-∞, 4) U (4, ∞)
The range is (-∞, ∞)
If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.
take the absolute value of the coefficient (2)
then the lower bound is the negative of that (-2)
so the range is [-2,2]
Take into account, that in general, a cosine function of amplitude A, period T and vertical translation b, can be written as follow:
In the given case, you have:
A = 4
T = 3π/4
b = -3
By replacing you obtain:
Hence, the answer is:
f(x) = 4cos(8/3 x) - 3
<span>the answer to 1.47 divided by 3.5 is 0.42. When you use different power of 10 to multiply the dividend and the divisor, the answer changes to different multiples of 0.42 in terms of 10. The answer could be 0.042 or 4.2 etc depending on the power of 10 used to multiply the dividend and divisor.</span>
