Modulus functions and transformations · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Linear modulus graphs and inequalities — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \left|{x - 23}\right| + 2\). Here \(\displaystyle a=2, h=23, k=2, d=2\).

Find the x-coordinate of the vertex.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Linear modulus graphs and inequalities — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 \left|{x - 24}\right| + 3\). Here \(\displaystyle a=3, h=24, k=3, d=3\).

Find the x-coordinate of the vertex.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Linear modulus graphs and inequalities — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 \left|{x - 24}\right| + 3\). Here \(\displaystyle a=3, h=24, k=3, d=3\).

Find the least value of f.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Linear modulus graphs and inequalities — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = 4 \left|{x - 25}\right| + 4\). Here \(\displaystyle a=4, h=25, k=4, d=4\).

Find the least value of f.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Linear modulus graphs and inequalities — objective 3

Maths4U Original · Short practice

\(f{\left(x \right)} = 4 \left|{x - 25}\right| + 4\). Here \(\displaystyle a=4, h=25, k=4, d=4\).

Find the larger solution of f(x)=k+ad.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Linear modulus graphs and inequalities — objective 3

Maths4U Original · Short practice

\(f{\left(x \right)} = \left|{x - 26}\right| + 5\). Here \(\displaystyle a=1, h=26, k=5, d=2\).

Find the larger solution of f(x)=k+ad.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Linear modulus graphs and inequalities — objective 4

Maths4U Original · Short practice

\(f{\left(x \right)} = \left|{x - 26}\right| + 5\). Here \(\displaystyle a=1, h=26, k=5, d=2\).

Find the length of the interval where f(x)<k+ad.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Linear modulus graphs and inequalities — objective 4

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \left|{x - 27}\right| + 1\). Here \(\displaystyle a=2, h=27, k=1, d=3\).

Find the length of the interval where f(x)<k+ad.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

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