Find the constants a and b such that the function is continuous on the entire real line. $ f(x) = \left\{\begin{array}{ll} {\color{red}5}, & x \leq -{\color{red}2}\\ ax + b, & -{\color{red}2} < x < {\color{red}3}\\ -{\color{red}5}, & x \geq {\color{red}3} \end{array}\right. $

we are given

piecewise function as

f(x) =5  when x<=-2

f(x)=ax+b  when -2<x<3

f(x)=-5 when x>=3

We are given f(x) is continuous for all values of x

so, it will also be continuous at x=-2 and x=3

Continuity at x=-2:

Value of both functions must be same at x=-2

so, we get

Continuity at x=3:

Value of both functions must be same at x=3

so, we get

so, we get system of equation as

now, we can subtract both equations

and we get

now, we can find b

so, we get

..............Answer

Step-by-step explanation:

Hello!

The FMA Company designed a new type of bowling ball and want to test if the new bowling average differs from the bowling average of the old model. Symbolically μ≠155

Sample:

n= 120 men bowling in scratch leagues

sample mean x[bar]= 170

variance δ²= 100

The hypothesis is:

H₀:μ=155

H₁:μ≠155

α: 0.05

The statistic to use for this hypothesis, assuming that the variable has a normal distribution.

Z= x[bar]-μ ≈ N(0;1)

δ/√n

The critical region for this test is two-tailed, this means you'll reject the null hypothesis to small or big values of the statistic.

= = -1.96

= = 1.96

You'll reject the null hypothesis to values of Z≤-1.96 or Z≥1.96.

Under the null Hypothesis the statistic value is:

Z= x[bar]-μ

δ/√n

Z= 170-155

10/√120

Z= 15/0.913 = 16.42

Decision: Reject the null Hypothesis.

I hope you have a SUPER day!