f(x)={2x,x<1}
{5,x=1}
{x^2,x>1}
Given the piecewise functions shown below, select all of the statements that are true.
A.f(5)=1
B.f(2)=4
C.f(-2)=4
D.f(1)=5
F(1)=5 and f(2)=4
GRAPH IT !!!!!
when x = 5 , f(5) = 25
when x = 2 , f(2) = 4 check
when x = -2 , f(-2) = -4
when x = 1 , f(1) = 5 check
f(1)=5
To determine which statements are true, we need to evaluate the given piecewise function at the specified values.
The piecewise function is:
f(x) = {
2x , x < 1
5 , x = 1
x^2 , x > 1
}
A. f(5) = 1
To evaluate f(5), we need to check which condition applies to x = 5. Since x = 5 is greater than 1, we use the third part of the function, which is x^2.
f(5) = 5^2 = 25
Therefore, statement A (f(5) = 1) is false.
B. f(2) = 4
To evaluate f(2), we check the condition that applies to x = 2. Since 2 is greater than 1, we use the third part of the function, which is x^2.
f(2) = 2^2 = 4
Therefore, statement B (f(2) = 4) is true.
C. f(-2) = 4
To evaluate f(-2), we check the condition that applies to x = -2. Since -2 is less than 1, we use the first part of the function, which is 2x.
f(-2) = 2(-2) = -4
Therefore, statement C (f(-2) = 4) is false.
D. f(1) = 5
To evaluate f(1), we check the condition that applies to x = 1. Since x = 1 satisfies the second part of the function, which is 5.
f(1) = 5
Therefore, statement D (f(1) = 5) is true.
In summary, the true statements are:
B. f(2) = 4
D. f(1) = 5