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Hello, I need some assistance with this homework question please for precalculusHW Q7

Hello, I need some assistance with this homework question please for precalculusHW-example-1
User Bhargav Patel
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1 Answer

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Yes. (The graph is that of a function)

(a) A. Domain: ]-∞,∞[. Range: [-4,∞[

(b) A. The intercepts are (-5,0) , (-1,0) and (0,5)

Step-by-step explanation:

The vertical line test is a method to determine if a graph is a function by looking at its amount of intercepts with a random vertical. If there is more than one intercept with the random vertical line it isn't the graph of a function.

Here if you trace a random vertical line at any point of the graph you'll notice that it only intercepts it once. Hence it is a function's graph.

(a)

. The domain is given by the x-axis

On the graph, x can be any number: ]-∞,∞[

. The range is given by the y-axis

On the graph, y can be any number starting from -4 to higher : [-4,∞[

(b)

Intercepts are where the graph touches the x or y axis.

. The graph intercepts with the horizontal line (x-axis), at the point (-5,0) and (-1,0) : Notice y is = 0

. The graph intercepts with the vertical line (y-axis), at the point (0,5) : Notice x is = 0

NB:

When using intervals ∞ is always excluded. Because it is impossible to reach infinity,

User Luyin Sun
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