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# Eleventh Grade (Grade 11) Function and Algebra Concepts Questions

You can create printable tests and worksheets from these Grade 11 Function and Algebra Concepts questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

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Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. $f(x) = 4x^3 + 2$
1. $f^{-1}(x) = (x^3-2)/4$
2. $f^{-1}(x) = (root[3](x) - 2)/4$
3. $f^{-1}(x) = root[3]((x-2)/4)$
4. $f^{-1}(x) = root[3](x-2)/4$
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Add the complex numbers. $(-3+7i) + (3 - i)$
1. $6i$
2. $6 + 8i$
3. $-6 + 6i$
4. $6 + 6i$
Grade 11 Exponents
Solve. $5^(3x-1)*5^(2x-5)=5^(x+6)$
1. $x = 0$
2. $x = 1/5$
3. $x = 2$
4. $x = 3$
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
Grade 11 Exponents
Solve for $x$. $3^(2x) = 27^(4)$
1. $6$
2. $7/2$
3. $32$
4. $4$
Grade 11 Exponents
Solve. $64^x=8^(3x+1)$
1. $x = 1$
2. $x = -1$
3. $x = 1/5$
4. $x = -1/5$
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Looking at the graph of a quadratic polynomial, roots or zeros correspond to where the graph crosses the x-axis. When the graph just touches the x-axis, this corresponds to a double root. The Fundamental Theorem of Algebra states that a quadratic polynomial will always have 2 roots. How is this reconciled with a quadratic polynomial whose graph does not intersect the x-axis?
1. Quadratic polynomials always intersect the x-axis.
2. If a quadratic polynomial doesn't cross the x-axis it is no longer a polynomial, and the Fundamental Theorem of Algebra no longer applies.
3. When a quadratic polynomial doesn't cross the x-axis, this simply implies that its roots are complex with non-zero imaginary parts.
4. Simply translate the quadratic polynomial till it does cross the x-axis.
Grade 11 Polynomials and Rational Expressions
Factor the following polynomial.

$x^3-x^2-8x+12$
1. $(x+3)(x-2)^2$
2. $(x+3)(x-2)(x+1)$
3. $(x-3)(x+1)(x-5)$
4. $(x-1)(x-2)(x+4)$
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Jeremy is working with the Fundamental Theorem of Algebra, and thinks he's found an exception. Looking at $f(x) = 4(x-1)^2$, this will result in only one root, $x=1$. Therefore, despite this being a second degree polynomial, there is only one root. Is this correct?
1. Yes, this is a known exception.
2. No, this is not a polynomial, it is a quadratic function.
3. No, if the quadratic formula is used, the other root is found.
4. No, this root has multiplicity of 2, which means it counts as two roots.
Grade 11 Linear Equations CCSS: HSF-LE.A.1, HSF-LE.A.1a
Given the table below, which lists some of the values of the function $f(x)$, which of the following is true, and why?

 $\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$ $0$ $-4$ $2$ $2$ $4$ $8$ $6$ $14$ $8$ $20$
1. $f(x)$ is linear, because the difference of y-values over equal intervals is constant.
2. $f(x)$ is linear, because the difference of x-values is constantly 2 units.
3. $f(x)$ is exponential, because the ratio of y-values over equal intervals is constant.
4. It cannot be determined whether $f(x)$ is linear or exponential, because there are no intervals of only one unit in the table.
Grade 11 Logarithms CCSS: HSF-BF.B.5, HSF-LE.A.4
$2^x=64$ is equivalent to which of the following?
1. $log_64 x=2$
2. $log_2 64=x$
3. $log_2 x=64$
4. $log_x 64=2$
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Subtract the complex numbers. $3i - (-5 + 3i)$
1. $5$
2. $-5 - 6i$
3. $5 + 6i$
4. $-5$
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Write the expression as a complex number in standard form.

$(3 - 5i)(1 + 3i)$
1. $3 - 15i$
2. $-2i + 4i$
3. $18 + 4i$
4. $15 - 2i$
Grade 11 Functions and Relations CCSS: HSF-IF.B.5
What is the domain and range of the graphed function?
1. Domain and range are all real numbers.
2. Domain is all real numbers less than zero and range is all real numbers.
3. Domain is all real numbers and range is all real numbers equal to or less than zero.
4. None of the above.
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