f(x)=4x+3 is linear.
Being linear means to be arranged in or extending along a straight or nearly straight line. We can test whether the function is linear or not with its slope, which is its first derivative. First, let y=f(x)=4x+3, its derivative is dy/dx=4 (a constant), so it is a linear function with a constant slope. If it is an exponential function, its slope should be monotonically changed.