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which statements can be made to compare and contrast the graphs of ( x leq 4 ) and ( x > 4 )? select all that apply.

a) both graphs have endpoints at 4.

b) both graphs have endpoints at 0.

c) the graph of ( x leq 4 ) has a dot at 4 with an arrow pointing to the left.

d) the graph of ( x leq 4 ) has a dot at 4 with an arrow pointing to the right.

e) the graph of ( x > 4 ) has a dot with an arrow pointing to the left.

f) the graph of ( x > 4 ) has a dot with an arrow pointing to the right.

g) the graph of ( x > 4 ) has an open circle with an arrow pointing to the left.

h) the graph of ( x > 4 ) has an open circle with an arrow pointing to the right.

Explanation:

Step1: Analyze \( x \leq 4 \) graph

For \( x \leq 4 \), the inequality includes 4, so we use a closed dot (filled circle) at 4. The values of \( x \) are less than or equal to 4, so the arrow points to the left (towards smaller numbers). So option C is correct, D is wrong.

Step2: Analyze \( x > 4 \) graph

For \( x > 4 \), the inequality does not include 4, so we use an open circle (not filled) at 4. The values of \( x \) are greater than 4, so the arrow points to the right (towards larger numbers). So option H is correct, E, F, G are wrong.

Step3: Analyze endpoint claims

• Option A: \( x \leq 4 \) has a closed dot at 4, \( x > 4 \) has an open circle at 4. So they both have a "point" (dot or circle) at 4. So A is correct.
• Option B: Neither graph has an endpoint at 0. So B is wrong.

Answer:

A) Both graphs have endpoints at 4, C) The graph of \( x \leq 4 \) has a dot at 4 with an arrow pointing to the left, H) The graph of \( x > 4 \) has an open circle with an arrow pointing to the right