1.
Item 1. Which type of graph is this?
Solution:The graph shown has the general shape of a cubic function.A cubic graph usually has opposite end behaviour: one end goes down while the other end goes up, or one end goes up while the other end goes down.Therefore, the graph is cubic.Answer: B
2.
Item 4. Write the equation of the graph after it has been compressed vertically by a factor of \(\frac{5}{13}\) from the original graph of \(y=\sqrt{3(x+2)}\).
Solution:A vertical compression by a factor of \(\frac{5}{13}\) means all \(y\)-values are multiplied by \(\frac{5}{13}\).Start with:\[y=\sqrt{3(x+2)}\]Multiply the function by the compression factor:\[y=\frac{5}{13}\sqrt{3(x+2)}\]Therefore, the transformed equation is \(y=rac{5}{13}\sqrt{3(x+2)}\).Answer: D
3.
Item 5. Four graphs of functions in the form \(y=ax^4\) are shown. The graph representing the function with the smallest value of \(a\) is:
Solution:For functions in the form \(y=ax^4\), the value of \(a\) affects vertical stretch or compression.A smaller positive value of \(a\) makes the graph wider and shorter, which means a vertical compression.Among the four graphs, graph I is the widest and shortest for the same change in \(x\).Therefore, graph I has the smallest value of \(a\).Answer: A
4.
Item 2. Which function notation fits best the following statement? Function \(h\) in terms of \(x-5\).
Solution:The statement says function \(h\), so the function name must be \(h\).The phrase “in terms of \(x-5\)” means \(x-5\) goes inside the brackets.Therefore, the correct notation is:\[h(x-5)\]Answer: E
5.
Item 3. Solve \((-3)+(+5)\).
Solution:Add the two integers:\[(-3)+(+5)=-3+5\]\[-3+5=2\]Therefore, the value is \(2\).Answer: B
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