Solve first for the solution of the inequalities. This can be done by replacing first the inequalities sign with the equal sign.

x + y = 1
2y = x - 4

The values of x and y from the system of linear equation are 2 and -1. This means that the intersection of the lines should be at point (2, -1).

Substitute 3 to x and determine the value of y from the second inequality.
2y ≥ x - 4

Substituting,
2y ≥ 3 - 4, y ≥ -1/2

Hence, the solution to this item should be the fourth one.

6 0

3 years ago

Please show your work this question what made you come to the conclusion. Thank you

AveGali [126]

Answer:

B the range, the x- and y-intercept

Step-by-step explanation:

the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).

but the range changes, as for the original function y could only have positive values - even for negative x.

the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.

the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.

the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.

the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.

the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)

$3 {b}^{x + 1} = 2$