Math 1 1st Quarter Practice Assessment

The given function is a rational function because it is in the form of a fraction, where both the numerator and the denominator are polynomials. In this case, the function may have variables in the numerator and/or the denominator, and the degree of the numerator can be different from the degree of the denominator.

Interval of increase is the values of x at which the function is increasing (going uphill). This function does not begin increasing until x=3 and continues to forever (oo).

Radicand and index must be the same when adding or subtracting radical expressions. In this case they are, so all you need to do is subtract coefficients and rewrite the radical.

S(6) is the sixth term. Three is being subtracted to find the next term. Therefore, you get 13, 10, 7, 4, 1, -2. The sixth term here is -2.

X is always the independent quantity and you are told that x represents the number of hours worked in a month.

The largest perfect square in 48 is 16 and the largest perfect square in x^3 is x^2. So you get sqrt(16*3*x^2*x). The square root of 16 is 4 and the square root of x^2 is x, leaving 3 and x under the radical. Hence, your answer is 4xsqrt(3x).

(-) Reflection across the x-axis
(+5) Left five

c represents the number of cases sold and p(c) represents the profit. In p(6)= 108, c has been replaced with 6 and p(c) = 108, therefore 6 represents the number of cases sold and 108 is the profit.

Use long division.

You must plug -2 in for x in the function. Square -2 first and get 4. Multiply 4 by -2 and get -8. Add 1 to -8 and get -7.

The function described in the question does not have a constant rate of change. This means that the rate at which the function is changing is not consistent throughout its domain. Instead, the rate of change is increasing, indicating that the function is becoming steeper or more steeply sloped as the input values increase. Therefore, the statement "The rate of change is constant" is not true for this function.

FOIL - You must multiply the first terms in each parenthesis, then the outer terms, then the inner terms, then the last terms. Then combine any like terms.

Since this is a quadratic with a range of all real numbers greater than or equal to negative one, it has a vertex at (0,-1) and is opening upward. Therefore the function crosses the x-axis twice.

Rate of Change: (Change in Y)/(Change in X)

x = -5 -2, Plug both values into g(x) = 3x^2 to get y
y = 75 12

Change in Y = 75 - 12 = 63
Change in X = -5 - -2 = -3

63/-3 = -21

t0 is the first term of a sequence. Therefore n=1, so we need to find S(1). When you plug 1 in for n, you get 4^3, which is 64.

A vertical reflection flips a function across the x-axis, which means that the positive values of the function become negative and vice versa. This transformation does not involve any movement along the x-axis or a change in the shape of the function, only a reflection across the x-axis. Therefore, the correct answer is Vertical Reflection.

Change the subtraction to addition, and change the sign of everything in the parenthesis to the right. Then add like terms.
(-14x^3 - 9x + 3) + (-5x^2 - 3x + 1)

A cubic function is the only parent function that has a domain of all real numbers and a range of all real numbers. This is because a cubic function is a polynomial function of degree 3, which means it can take on any real number as input and produce any real number as output. Linear, quadratic, absolute value, and square root functions all have restrictions on their domains and ranges, so they do not meet the given criteria.

Distribute the -2sqrt(3) to both sqrt(3) and 5. Then simplify.

You must first subtract 3 from 12, which gives you 9. Then take the square root of 9, which is 3. The 3 then becomes negative, giving you -3. Lastly, you must add 2 to -3, which is -1.