Question Video: Determining the Sign of a Linear Function | Nagwa Question Video: Determining the Sign of a Linear Function | Nagwa

# Question Video: Determining the Sign of a Linear Function Mathematics • First Year of Secondary School

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Determine the sign of the function 𝑓(𝑥) = −5𝑥 + 5.

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### 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.

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