Which statement describes the end behavior of the exponential function f(x) = 2x – 3? a for very high x-values, f(x) moves toward positive infinity. b for very high x-values, f(x) moves toward negative infinity. c for very high x-values, f(x) moves toward the horizontal asymptote. d for very low x-values of x, f(x) moves toward negative infinity.

The correct answer is a. for very high x-values, f(x) moves towards positive infinity.

This can always be determined by two factors.

1) is it linear or something else?

2) Is the lead coefficient positive or negative.

In this case, since the x is not being raised to a power or is not raised to a power itself, we know that there are no asymptotes. That takes care of #1 for us.

As for #2, since the coefficient of x (which is the highest power here) is positive, that means it continues to get bigger. If it were negative it would be the opposite. So, the correct answer is that as x gets bigger, f(x) moves towards positive infinity.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is