Question Video: Identifying the Points of Intersection of a Linear Function with the 𝑥-axis and 𝑦-axis | Nagwa Question Video: Identifying the Points of Intersection of a Linear Function with the 𝑥-axis and 𝑦-axis | Nagwa

Question Video: Identifying the Points of Intersection of a Linear Function with the 𝑥-axis and 𝑦-axis Mathematics • Third Year of Preparatory School

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Consider the function 𝑓 : ℝ ⟶ ℝ, 𝑓(𝑥) = 2𝑥 − 4. Its graph is given in the following diagram. At which point does the graph of 𝑓 intersect the 𝑥-axis? At which point does the graph of 𝑓 intersect the 𝑦-axis?

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Video Transcript

Consider the function 𝑓 that maps real values onto real values, where 𝑓 of 𝑥 is equal to two 𝑥 minus four. Its graph is given in the following diagram. At which point does the graph of 𝑓 intersect the 𝑥-axis? At which point does the graph of 𝑓 intersect the 𝑦-axis?

There are two parts to this question. We need to find the points at which the graph of 𝑓 crosses the 𝑥- and 𝑦-axis. We can do this directly from the diagram by inspection. The graph intersects the 𝑥-axis when 𝑥 is equal to two. This point has coordinates two, zero. The graph intersects the 𝑦-axis at 𝑦 is equal to negative four. This point has coordinates zero, negative four.

Whilst this is the easiest way to answer this question, we could also do so without the graph. If we consider the function 𝑓 of 𝑥 is equal to two 𝑥 minus four, we know that the graph will intersect the 𝑥-axis when 𝑓 of 𝑥 is equal to zero. This means that two 𝑥 minus four equals zero. We can solve this equation by adding four to both sides and then dividing through by two such that 𝑥 is equal to two. This confirms our answer to the first part of the question, the coordinate two, zero.

We also know that when a function intersects the 𝑦-axis, 𝑥 is equal to zero. Calculating 𝑓 of zero gives us two multiplied by zero minus four. As this is equal to negative four, this confirms that the graph of 𝑓 intersects the 𝑦-axis at the point zero, negative four.

The answers to the two parts of the question are two, zero and zero, negative four.

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