Question

drag the tiles to the correct boxes to complete the pairs. match each function to its domain. $f(x)=sqrt{x - 5}$ $f(x)=\frac{7}{x - 8}$ $f(x)=sqrt{x}$ $f(x)=8x$ all positive real numbers and 0 all real number greater than or equal to 5 all real numbers all real numbers except 8

Explanation:

Step1: Analyze \( f(x) = \sqrt{x - 5} \)

For a square root function \( \sqrt{u} \), the expression inside the square root (\( u \)) must be non - negative. So, \( x - 5\geq0 \), which implies \( x\geq5 \). So the domain of \( f(x)=\sqrt{x - 5} \) is all real numbers greater than or equal to 5.

Step2: Analyze \( f(x)=\frac{7}{x - 8} \)

For a rational function \( \frac{a}{b} \), the denominator \( b
eq0 \). So, \( x - 8
eq0 \), which means \( x
eq8 \). So the domain of \( f(x)=\frac{7}{x - 8} \) is all real numbers except 8.

Step3: Analyze \( f(x)=\sqrt{x} \)

For the square root function \( \sqrt{x} \), the expression inside the square root \( x\) must be non - negative (i.e., \( x\geq0 \)). So the domain of \( f(x)=\sqrt{x} \) is all positive real numbers and 0.

Step4: Analyze \( f(x) = 8x \)

For a linear function of the form \( y = mx + c\) (here \( m = 8\) and \( c = 0\)), there are no restrictions on the value of \( x\). So the domain of \( f(x)=8x \) is all real numbers.

Answer:

• \( f(x)=\sqrt{x - 5} \) pairs with "all real number greater than or equal to 5"
• \( f(x)=\frac{7}{x - 8} \) pairs with "all real numbers except 8"
• \( f(x)=\sqrt{x} \) pairs with "all positive real numbers and 0"
• \( f(x)=8x \) pairs with "all real numbers"