Question

mat100 - algebra i s1 (algebra i-aaa02)
the cube root function
identifying points on the graph of the cube root function
which points are on the graph of $f(x) = \sqrt3{x}$? choose three correct answers
(1, 1)
(-1, 1)
(0, 0)
(-27, -3)
(3, 27)

Explanation:

Step1: Check point (1,1)

Substitute \(x = 1\) into \(f(x)=\sqrt[3]{x}\). We get \(f(1)=\sqrt[3]{1}=1\). So (1,1) is on the graph.

Step2: Check point (-1,1)

Substitute \(x = - 1\) into \(f(x)=\sqrt[3]{x}\). We get \(f(-1)=\sqrt[3]{-1}=-1
eq1\). So (-1,1) is not on the graph.

Step3: Check point (0,0)

Substitute \(x = 0\) into \(f(x)=\sqrt[3]{x}\). We get \(f(0)=\sqrt[3]{0}=0\). So (0,0) is on the graph.

Step4: Check point (-27,-3)

Substitute \(x=-27\) into \(f(x)=\sqrt[3]{x}\). We get \(f(-27)=\sqrt[3]{-27}=-3\). So (-27,-3) is on the graph.

Step5: Check point (3,27)

Substitute \(x = 3\) into \(f(x)=\sqrt[3]{x}\). We get \(f(3)=\sqrt[3]{3}
eq27\). So (3,27) is not on the graph.

Answer:

(1, 1), (0, 0), (-27, -3)