Video Transcript
Determine the sign of the function
𝑓 of 𝑥 is equal to negative five 𝑥 plus five.
We know that this function is
linear as it is of the form 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is the gradient or
slope and 𝑏 is the 𝑦-intercept. In our question, the slope of the
function is negative five and the 𝑦-intercept is five. As the slope of the function is
negative, our graph will slope down to the right. In order to determine the sign of
the function, we need to find out where the graph is positive, negative, and also
equal to zero. We can see that the graph crosses
the 𝑥-axis at one point. This will be the point where the
function is equal to zero. When the graph is above the
𝑥-axis, the function will be positive, and when it is below the 𝑥-axis, it will be
negative.
To calculate the point at which the
function is equal to zero, we will set 𝑓 of 𝑥 equal to zero. Adding five 𝑥 to both sides of
this equation gives us five 𝑥 is equal to five. We can then divide both sides of
this equation by five, giving us 𝑥 is equal to one. Our function is positive for all
𝑥-values less than one. The function is negative or below
the 𝑥-axis for all 𝑥-values greater than one. We can therefore conclude the
following. The function is positive when 𝑥 is
less than one, the function is negative when 𝑥 is greater than one, and, finally,
the function equals zero when 𝑥 equals one. The function 𝑓 of 𝑥 equals
negative five 𝑥 plus five is positive, negative, and equals zero for different
values of 𝑥.
