C

9000007202

Level: 
C
Consider the function f(x)=[x]+3 on the domain Dom⁡(f)=(1;2). Find the parameters a and b and a domain of the linear function g:y=ax+b which ensure that f and g are identical functions. Hint: The function y=[x] is a floor function: the largest integer less than or equal to x. For positive x it is also called the integer part of x.
a=0, b=4; Dom⁡(g)=(1;2)
a=0, b=3; Dom⁡(g)=(1;2)
a=3, b=0; Dom⁡(g)=(1;2)
a=−3, b=0; Dom⁡(g)=(1;2)

9000007203

Level: 
C
Consider the function f(x)=sgn⁡(x−2) defined on Dom⁡(f)=R−. Find the parameters a a b and domain of the linear function g(x)=ax+b which ensure that f and g are identical functions. Hint: The function y=sgn⁡(x) is the sign function. The values of sign function is 1 for each positive x, −1 for each negative x and 0 if x=0.
a=0, b=−1; Dom⁡(g)=R−
a=0, b=1; Dom⁡(g)=R+
a=1, b=0; Dom⁡(g)=R−
a=−1, b=0; Dom⁡(g)=R+

9000007207

Level: 
C
Identify a function which has the following three properties: it has at least one minimum or maximum, it is an increasing function and the range of this function is the set of all nonnegative numbers.
f(x)=2x−2, x∈[1;+∞)
f(x)=2x+2, x∈(−1;+∞)
f(x)=−2x+2, x∈(−∞;1]
f(x)=−2x−2, x∈R

9000007208

Level: 
C
Paul's home is 6km from the school. At the time t=0 Paul starts to walk from his home to the school along a straight street at a constant velocity 5km/h. Find the function which describes Paul's remaining distance to the school as a function of time.
s=6−5t
s=5t−6
s=5t
s=5t+6