Wgu D667 – Precalculus | Objective
Assessment | (Oa) V1 And V2 | 2026
Update | Actual Questions And Answers
With Complete Solution
Question 1
If \(f(x)=3x^2-4x+1\), what is \(f(-2)\)?
A. 9
B. 17
C. 21
D. 25
Correct Answer: C. 21
Rationale:
Substitute \(x=-2\):
\[ f(-2)=3(-2)^2-4(-2)+1 \]\[ =3(4)+8+1=12+8+1=21 \]
Therefore, \(f(-2)=21\).
Question 2
Which of the following represents a function?
A. \(x=y^2\)
B. \(x^2+y^2=9\)
C. \(y^2=x+4\)
D. \(x=4\)
Correct Answer: A. \(x=y^2\)
Rationale:
Rewrite A as:
\[ y=\pm\sqrt{x} \]
,Actually, this produces two \(y\)-values for most positive \(x\), so A is not a function of \(x\).
Let's examine the choices carefully. The correct choice is D? A vertical line \(x=4\) is not a
function of \(x\) either. Therefore, none of the choices as written is a function of \(x\).
A properly constructed question should have one valid answer. Thus, the intended correction is:
Correct Answer: None of the above.
For OA preparation, remember: a relation is a function of \(x\) if every \(x\)-value corresponds
to exactly one \(y\)-value.
Question 3
What is the domain of
\[ f(x)=\frac{1}{x-5}? \]
A. \(x>5\)
B. \(x<5\)
C. All real numbers except \(5\)
D. All real numbers
Correct Answer: C. All real numbers except 5
Rationale:
A rational function is undefined when its denominator equals zero:
\[ x-5=0 \]\[ x=5 \]
Therefore,
\[ \boxed{x\neq5} \]
The domain is:
\[ (-\infty,5)\cup(5,\infty) \]
Question 4
What is the range of
\[ f(x)=x^2+3? \]
,A. \(y\ge3\)
B. \(y>3\)
C. \(y\le3\)
D. All real numbers
Correct Answer: A. \(y\ge3\)
Rationale:
Since \(x^2\ge0\),
\[ x^2+3\ge3 \]
The minimum value is 3, occurring at \(x=0\). Therefore the range is:
\[ \boxed{[3,\infty)} \]
Question 5
Which transformation changes \(f(x)\) into \(f(x-4)\)?
A. Shift left 4 units
B. Shift right 4 units
C. Shift up 4 units
D. Shift down 4 units
Correct Answer: B. Shift right 4 units
Rationale:
Horizontal transformations work opposite to the sign inside the function:
\[ f(x-h) \]
shifts the graph right \(h\) units.
Therefore:
\[ f(x-4) \]
shifts the graph 4 units to the right.
Question 6
If
, \[ f(x)=2x+3 \]
and
\[ g(x)=x^2, \]
what is \((f\circ g)(2)\)?
A. 7
B. 11
C. 14
D. 19
Correct Answer: B. 11
Rationale:
\[ (f\circ g)(2)=f(g(2)) \]
First:
\[ g(2)=2^2=4 \]
Then:
\[ f(4)=2(4)+3=11 \]
Therefore:
\[ \boxed{11} \]
Question 7
What is the inverse of
\[ f(x)=3x-7? \]
A. \(f^{-1}(x)=\frac{x-7}{3}\)
B. \(f^{-1}(x)=\frac{x+7}{3}\)
C. \(f^{-1}(x)=3x+7\)
D. \(f^{-1}(x)=\frac{7-x}{3}\)
Correct Answer: B. \(\frac{x+7}{3}\)
Rationale:
Start with:
Assessment | (Oa) V1 And V2 | 2026
Update | Actual Questions And Answers
With Complete Solution
Question 1
If \(f(x)=3x^2-4x+1\), what is \(f(-2)\)?
A. 9
B. 17
C. 21
D. 25
Correct Answer: C. 21
Rationale:
Substitute \(x=-2\):
\[ f(-2)=3(-2)^2-4(-2)+1 \]\[ =3(4)+8+1=12+8+1=21 \]
Therefore, \(f(-2)=21\).
Question 2
Which of the following represents a function?
A. \(x=y^2\)
B. \(x^2+y^2=9\)
C. \(y^2=x+4\)
D. \(x=4\)
Correct Answer: A. \(x=y^2\)
Rationale:
Rewrite A as:
\[ y=\pm\sqrt{x} \]
,Actually, this produces two \(y\)-values for most positive \(x\), so A is not a function of \(x\).
Let's examine the choices carefully. The correct choice is D? A vertical line \(x=4\) is not a
function of \(x\) either. Therefore, none of the choices as written is a function of \(x\).
A properly constructed question should have one valid answer. Thus, the intended correction is:
Correct Answer: None of the above.
For OA preparation, remember: a relation is a function of \(x\) if every \(x\)-value corresponds
to exactly one \(y\)-value.
Question 3
What is the domain of
\[ f(x)=\frac{1}{x-5}? \]
A. \(x>5\)
B. \(x<5\)
C. All real numbers except \(5\)
D. All real numbers
Correct Answer: C. All real numbers except 5
Rationale:
A rational function is undefined when its denominator equals zero:
\[ x-5=0 \]\[ x=5 \]
Therefore,
\[ \boxed{x\neq5} \]
The domain is:
\[ (-\infty,5)\cup(5,\infty) \]
Question 4
What is the range of
\[ f(x)=x^2+3? \]
,A. \(y\ge3\)
B. \(y>3\)
C. \(y\le3\)
D. All real numbers
Correct Answer: A. \(y\ge3\)
Rationale:
Since \(x^2\ge0\),
\[ x^2+3\ge3 \]
The minimum value is 3, occurring at \(x=0\). Therefore the range is:
\[ \boxed{[3,\infty)} \]
Question 5
Which transformation changes \(f(x)\) into \(f(x-4)\)?
A. Shift left 4 units
B. Shift right 4 units
C. Shift up 4 units
D. Shift down 4 units
Correct Answer: B. Shift right 4 units
Rationale:
Horizontal transformations work opposite to the sign inside the function:
\[ f(x-h) \]
shifts the graph right \(h\) units.
Therefore:
\[ f(x-4) \]
shifts the graph 4 units to the right.
Question 6
If
, \[ f(x)=2x+3 \]
and
\[ g(x)=x^2, \]
what is \((f\circ g)(2)\)?
A. 7
B. 11
C. 14
D. 19
Correct Answer: B. 11
Rationale:
\[ (f\circ g)(2)=f(g(2)) \]
First:
\[ g(2)=2^2=4 \]
Then:
\[ f(4)=2(4)+3=11 \]
Therefore:
\[ \boxed{11} \]
Question 7
What is the inverse of
\[ f(x)=3x-7? \]
A. \(f^{-1}(x)=\frac{x-7}{3}\)
B. \(f^{-1}(x)=\frac{x+7}{3}\)
C. \(f^{-1}(x)=3x+7\)
D. \(f^{-1}(x)=\frac{7-x}{3}\)
Correct Answer: B. \(\frac{x+7}{3}\)
Rationale:
Start with:
